Least Common Multiple (LCM) (Grade 6)
A multiple of a number is what you get by counting by it (multiples of 4: 4, 8, 12, 16…).
Understanding least common multiple
The least common multiple of two numbers is the smallest number that is a multiple of both. List the multiples of each and find the first one they share. The LCM is exactly what you need to find a common denominator when adding fractions.
Seeing it in action
Worked example
Find the LCM of 4 and 6.
Multiples of 4: 4, 8, 12, 16… Multiples of 6: 6, 12, 18…
The first shared multiple is 12.
12 is the first shared multiple of 4 and 6.
A common mistake, and the fix
Multiplying the two numbers and stopping.
4 × 6 = 24 is a common multiple of 4 and 6, but not the least one: 12 is a multiple of both (4 × 3 and 6 × 2). Listing a few multiples of each (4, 8, 12 and 6, 12) finds the first one they share.
Try a few
LCM of 3 and 5
multiples of 5: 5, 10, 15; 15 is the first that 3 divides.
LCM of 4 and 8
8 is already a multiple of 4.
LCM of 6 and 9
multiples of 9: 9, 18; 18 is the first that 6 divides.
Factor Fields
A calm number-theory game for factors, multiples, primes, GCF, and LCM.
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
Free printable · 3 pagesText version (screen-reader friendly): Draw it. Explain it. Math sample
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