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Least common multiple

Find the smallest positive multiple shared by two numbers.

Practice + answer key · 2 pages

Worksheet settings8 questions · 2 columns · A4
Starting-number range

Both positive starting values are drawn from the range.

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Least common multipleLeast common multiple. Practice. Find the least common multiple of 2 and 8. Find the least common multiple of 9 and 6. Find the least common multiple of 11 and 3. Find the least common multiple of 5 and 8. Find the least common multiple of 3 and 9. Find the least common multiple of 7 and 6. Find the least common multiple of 7 and 5. Find the least common multiple of 12 and 6.Name __________________________Date _______________Least common multipleFind the least common multiple of each pair.Worked exampleFind the least common multiple of 6 and 8. → 24The greatest common factor of 6 and 8 is 2.1.Find the least common multiple of2 and 8.2.Find the least common multiple of9 and 6.3.Find the least common multiple of11 and 3.4.Find the least common multiple of5 and 8.5.Find the least common multiple of3 and 9.6.Find the least common multiple of7 and 6.7.Find the least common multiple of7 and 5.8.Find the least common multiple of12 and 6.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 1mathsprig-1 · mathsprig-v1 · b29d7f02
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Practice + answer key · 2 pages

Factors & multiples

What you’ll practice

Calculate the least common positive multiple of two positive integers.

Look for the first number that both starting numbers divide into evenly. You can use their greatest common factor to find it without writing a long list of multiples.

How this skill works

A common multiple is divisible by both starting numbers. The least common multiple is the smallest positive such value.

For positive integers a and b, divide their product by their greatest common factor. This removes the shared factor counted twice in the product.

Worked example

Find the least common multiple of 6 and 8.
  1. The greatest common factor of 6 and 8 is 2.
  2. (6 × 8) ÷ 2 = 24.
  3. 24 ÷ 6 = 4 and 24 ÷ 8 = 3.

Answer: 24

Teaching notes

  • Distinguish a multiple from a factor before starting.
  • If one number already divides the other, the larger is the least common multiple.
Practice questions
  1. Find the least common multiple of 2 and 8.
  2. Find the least common multiple of 9 and 6.
  3. Find the least common multiple of 11 and 3.
  4. Find the least common multiple of 5 and 8.
  5. Find the least common multiple of 3 and 9.
  6. Find the least common multiple of 7 and 6.
  7. Find the least common multiple of 7 and 5.
  8. Find the least common multiple of 12 and 6.
Answers and steps
  1. 8
    1. The greatest common factor is 2. Divide out the shared part once: (2 × 8) ÷ 2 = 8.
    2. 8 ÷ 2 = 4 and 8 ÷ 8 = 1, so both numbers divide the result exactly.
  2. 18
    1. The greatest common factor is 3. Divide out the shared part once: (9 × 6) ÷ 3 = 18.
    2. 18 ÷ 9 = 2 and 18 ÷ 6 = 3, so both numbers divide the result exactly.
  3. 33
    1. The greatest common factor is 1. Divide out the shared part once: (11 × 3) ÷ 1 = 33.
    2. 33 ÷ 11 = 3 and 33 ÷ 3 = 11, so both numbers divide the result exactly.
  4. 40
    1. The greatest common factor is 1. Divide out the shared part once: (5 × 8) ÷ 1 = 40.
    2. 40 ÷ 5 = 8 and 40 ÷ 8 = 5, so both numbers divide the result exactly.
  5. 9
    1. The greatest common factor is 3. Divide out the shared part once: (3 × 9) ÷ 3 = 9.
    2. 9 ÷ 3 = 3 and 9 ÷ 9 = 1, so both numbers divide the result exactly.
  6. 42
    1. The greatest common factor is 1. Divide out the shared part once: (7 × 6) ÷ 1 = 42.
    2. 42 ÷ 7 = 6 and 42 ÷ 6 = 7, so both numbers divide the result exactly.
  7. 35
    1. The greatest common factor is 1. Divide out the shared part once: (7 × 5) ÷ 1 = 35.
    2. 35 ÷ 7 = 5 and 35 ÷ 5 = 7, so both numbers divide the result exactly.
  8. 12
    1. The greatest common factor is 6. Divide out the shared part once: (12 × 6) ÷ 6 = 12.
    2. 12 ÷ 12 = 1 and 12 ÷ 6 = 2, so both numbers divide the result exactly.