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AFCAT LCM and HCF — practice questions

Explore 4 free LCM and HCF questions in AFCAT Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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LCM and HCF questions and exercises with answers

Showing questions 1–4 of 4.

The HCF of 96 and 404 is 4. Their LCM is:Read the answer and worked solution →The LCM of 6, 72 and 120 is:Read the answer and worked solution →What is the HCF of 96 and 404?Read the answer and worked solution →The smallest number that is exactly divisible by every number from 1 to 10 is:Read the answer and worked solution →

Worked practice questions

The HCF of 96 and 404 is 4. Their LCM is:

  1. 8484
  2. 9696
  3. 4848
  4. 2424
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Correct answer: B. 9696

1. For any two numbers, HCF x LCM = the product of the two numbers. 2. Here the product is 96 x 404 = 38784. 3. So LCM = 38784 / 4. 4. That gives LCM = 9696. 5. A quick check: 9696 is divisible by both 96 and 404, which the smaller options are not. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_

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The LCM of 6, 72 and 120 is:

  1. 180
  2. 240
  3. 720
  4. 360
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Correct answer: D. 360

1. Write each number as a product of primes: 6 = 2 x 3. 2. 72 = 2^3 x 3^2 and 120 = 2^3 x 3 x 5. 3. The LCM takes the highest power of every prime that appears: 2^3, 3^2 and 5. 4. So LCM = 8 x 9 x 5 = 360. 5. 180 misses a factor of 2 and 240 misses a factor of 3, so neither is a multiple of 72. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_

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What is the HCF of 96 and 404?

  1. 2
  2. 8
  3. 4
  4. 12
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Correct answer: C. 4

1. Factorise both numbers into primes. 2. 96 = 2^5 x 3. 3. 404 = 2^2 x 101. 4. The common primes are only the 2s, and the lower power is 2^2. 5. So the HCF is 4. It cannot be 8 or 12, since 404 is not divisible by either. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_

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