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Number Systems • HCF & LCM Practice Drills (98 Qs)• Official Answer Keys

CAT HCF & LCM Practice Questions & Applications (95+ Questions)

Euclidean Algorithm, Bell Ringing Problems, Remainder Models with LCM, and Fraction HCF/LCM

98 Total Questions
MCQ: 80 (+3 / -1)
TITA: 18 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: HCF & LCM Practice Drills

HCF and LCM of FractionsFormula #1
\text{HCF} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}}, \quad \text{LCM} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}

Fractions must be in lowest simplified terms first.

Same Remainder ModelFormula #2
N = \text{LCM}(a, b, c) × k + r

Leaves remainder r when divided by a, b, or c.

Exam Hall Traps & Speedbreakers to Avoid
  • •Finding HCF/LCM of fractions before reducing them to their simplest coprime form.

Bite-Sized Practice Sets (9 Modules Available)

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Set 01: HCF/LCM

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Set 02: HCF/LCM

Difficulty: Moderate
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Set 03: HCF/LCM

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Set 04: HCF/LCM

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Set 05: HCF/LCM

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Set 06: HCF/LCM

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Set 07: HCF/LCM

Difficulty: Moderate
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Set 08: HCF/LCM

Difficulty: Hard
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Set 09: HCF/LCM

Difficulty: Moderate
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Official Exam Questions & Explanations (25 of 98)

Sorted in official convenor sequence
Question 1 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMEasy
What is the HCF of 48 and 180?
Practice More Questions
Official Correct Answer: A. Prime factorization of 48: $2^4 \times 3$; of 180: $2^2 \times 3^2 \times 5$. The HCF is the product of the lowest power of each prime factor present in both numbers: $2^2 \times 3 = 12$.
Question 2 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
The LCM of two numbers is 180 and their HCF is 12. If one of the numbers is 36, what is the other number?
Practice More Questions
Official Correct Answer: A. Let the numbers be $a$ and $b$. We know $LCM(a, b) \times HCF(a, b) = a \times b$. So, $180 \times 12 = 36 \times b$. Solving, $b = \frac{180 \times 12}{36} = 60$.
Question 3 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMHard
What is the smallest number that is a multiple of both 12 and 18 and is also a perfect square?
Practice More Questions
Official Correct Answer: B. The LCM of 12 and 18 is 36. The prime factorization of 36 is $2^2 \times 3^2$. To be a perfect square, all prime factors must have even powers. So, the smallest number is $2^2 \times 3^2 \times 2 \times 3 = 144$.
Question 4 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMEasy
What is the HCF of 56 and 14?
Practice More Questions
Official Correct Answer: C. Prime factorization of 56: $2^3 \times 7$; of 14: $2 \times 7$. The HCF is the product of the lowest power of each prime factor present in both numbers: $2 \times 7 = 14$.
Question 5 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the LCM of two numbers is 200 and their HCF is 25, what is the product of the two numbers?
Practice More Questions
Official Correct Answer: A. The product of two numbers is equal to the product of their LCM and HCF. So, the product is $200 \times 25 = 5000$.
Question 6 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMHard
If the HCF of two numbers is 12 and their LCM is 480, and one of the numbers is 24, what is the other number?
Practice More Questions
Official Correct Answer: B. Using the formula $HCF \times LCM = a \times b , where $a$ and $b$ are the two numbers. So, $12 \times 480 = 24 \times b$. Solving, $b = \frac{12 \times 480}{24} = 240 / 12 = 120$.
Question 7 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMEasy
What is the LCM of 35 and 45?
TITA Answer:
Practice More Questions
Official Correct Answer: 315. Prime factorization of 35: $5 \times 7$; of 45: $3^2 \times 5$. The LCM is the product of the highest power of each prime factor present in the numbers: $3^2 \times 5 \times 7 = 315$.
Question 8 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMEasy
The LCM of 4 and 6 is
TITA Answer:
Practice More Questions
Official Correct Answer: 12. The LCM of 4 and 6 is the smallest number that is a multiple of both 4 and 6. The multiples of 4 are 4, 8, 12, 16, etc., and the multiples of 6 are 6, 12, 18, 24, etc. The smallest common multiple is 12.
Question 9 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the HCF of two numbers is 12 and their LCM is 180, what is the product of the two numbers?
A
2160
B
2180
C
2200
D
2220
Practice More Questions
Official Correct Answer: A. The product of two numbers is equal to the product of their HCF and LCM. Therefore, the product is $12 \times 180 = 2160$.
Question 10 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMHard
If the HCF of two numbers is 14 and their LCM is 210, what is the product of the two numbers?
TITA Answer:
Practice More Questions
Official Correct Answer: 2940. The product of the two numbers is equal to the product of their HCF and LCM. Therefore, the product is $14 \times 210 = 2940$.
Question 11 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMEasy
The LCM of 8 and 12 is
TITA Answer:
Practice More Questions
Official Correct Answer: 24. The LCM of 8 and 12 is the smallest number that is a multiple of both 8 and 12. The multiples of 8 are 8, 16, 24, 32, etc., and the multiples of 12 are 12, 24, 36, 48, etc. The smallest common multiple is 24.
Question 12 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the HCF of two numbers is 7 and their LCM is 105, what is the sum of the two numbers?
A
28
B
35
C
42
D
49
Practice More Questions
Official Correct Answer: B. Let the two numbers be 7x and 7y, where x and y are coprime. Then, $7xy = 105 \implies xy = 15$. The possible pairs (x, y) are (3, 5) and (5, 3). Therefore, the numbers are 21 and 35, and their sum is 56/2 = 35.
Question 13 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMHard
If the HCF of two numbers is 3 and their LCM is 180, what is the product of the two numbers?
A
540
B
545
C
550
D
555
Practice More Questions
Official Correct Answer: A. The product of the two numbers is equal to the product of their HCF and LCM. Therefore, the product is $3 \times 180 = 540$.
Question 14 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
What is the HCF of 126and 168168?
Practice More Questions
Official Correct Answer: C. Factorize $126 = 2 \times 3^2 \times 7$ and $168 = 2^3 \times 3 \times 7$. The common factors are $2, 3,$ and $7$. Therefore, the HCF is $2 \times 3 \times 7 = 42$.
Question 15 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the LCM of two numbers is 120and their HCF is $10 , what is the product of the two numbers?
Practice More Questions
Official Correct Answer: A. The product of two numbers is equal to the product of their HCF and LCM. Therefore, the product is $10 \times 120 = 1200$.
Question 16 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
The HCF of two numbers is 12and their LCM is 180180. If one of the numbers is $36 , what is the other number?
Practice More Questions
Official Correct Answer: A. Using the formula HCF \times LCM = product of the numbers, we have $12 \times 180 = 36 \times \text{other number}$. Therefore, the other number is $60$.
Question 17 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
What is the LCM of 18and 2424?
Practice More Questions
Official Correct Answer: C. Prime factorize $18 = 2 \times 3^2$ and $24 = 2^3 \times 3$. The LCM is $2^3 \times 3^2 = 72$.
Question 18 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the HCF of two numbers is 14and their LCM is $280 , what is the product of the two numbers?
Practice More Questions
Official Correct Answer: A. Using the formula HCF \times LCM = product of the numbers, we have $14 \times 280 = 3920$.
Question 19 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
Find the LCM of $15 , 20 , and $35$.
TITA Answer:
Practice More Questions
Official Correct Answer: 140. Prime factorize $15 = 3 \times 5 , 20 = 2^2 \times 5 , and $35 = 5 \times 7$. The LCM is $2^2 \times 3 \times 5 \times 7 = 140$.
Question 20 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the HCF of two numbers is 12and their LCM is $360 , what is the product of the two numbers?
Practice More Questions
Official Correct Answer: A. Using the formula HCF \times LCM = product of the numbers, we have $12 \times 360 = 4320$. Therefore, the correct answer is $3600$.
Question 21 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
The LCM of two numbers is 48 and their HCF is 4. If one of the numbers is 12, what is the other number?
Practice More Questions
Official Correct Answer: B. We know that the product of two numbers is equal to the product of their HCF and LCM. Let the unknown number be $x$. So, $12 \times x = 4 \times 48$. Solving for $x , we get $x = \frac{4 \times 48}{12} = 16$. Therefore, the other number is 16.
Question 22 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the HCF of two numbers is 6 and their LCM is 180, what is the product of the two numbers?
Practice More Questions
Official Correct Answer: A. The product of two numbers is equal to the product of their HCF and LCM. So, the product of the two numbers is $6 \times 180 = 1080$.
Question 23 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
The HCF of two numbers is 12 and their LCM is 360. If one number is 60, what is the other number?
Practice More Questions
Official Correct Answer: A. Using the formula for the product of two numbers, $12 \times 360 = 60 \times x , we solve for $x$ and get $x = \frac{12 \times 360}{60} = 72$.
Question 24 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the HCF of two numbers is 15 and their LCM is 150, what is the product of the two numbers?
Practice More Questions
Official Correct Answer: A. The product of the two numbers is equal to the product of their HCF and LCM, which is $15 \times 150 = 2250$.
Question 25 of 98
ThinkCAT Practice SetQANumber Systems • HCF/LCMModerate
If the LCM of two numbers is 240 and their HCF is 8, what is the product of the two numbers?
Practice More Questions
Official Correct Answer: A. The product of the two numbers is equal to the product of their HCF and LCM, which is $8 \times 240 = 1920$.

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Frequently Asked Questions about CAT HCF & LCM Practice Questions & Applications (95+ Questions)

What concepts are covered in the HCF & LCM Practice Drills practice module?

This module covers HCF/LCM with 98 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for HCF & LCM Practice Drills questions?

The ideal target pace is 1.5 to 2.0 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for HCF & LCM Practice Drills?

Official past year exam questions are available in our CAT Number Systems PYQ Hub module.

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