Parent guide · 5 min read
Common multiples and the lowest common multiple for kids
A multiple is what you get by counting in steps of a number: the multiples of 6 are 6, 12, 18, 24 and so on. A common multiple is a number that appears in two lists at once, and the lowest common multiple (LCM) is the first one. Children are often handed this as a vocabulary list and a method to memorise. It is much easier to hold on to when it is a question with an answer: when will two repeating patterns land on the same number?
Try this tonight
4 things you can do at home
Start with a pattern your child can picture
One bus comes every 6 minutes and another every 8 minutes, and both just left. When do they leave together again? Ask your child to write the departure times for each bus and look for the first time that appears on both lists.
Write the multiples as a list, not in their head
Skip-count one number at a time and write each result down: 6, 12, 18, 24. Writing the list makes it easy to spot where the two lists meet and to see that a number found by accident is not necessarily the lowest.
Start the list with the bigger number
The LCM is never smaller than the larger of the two numbers. List the multiples of 8 first and check each one against 6: is 8 a multiple of 6? 16? 24? This is usually quicker than building both lists in full.
Check by dividing
Once there is an answer, divide it by each original number. 24 ÷ 6 = 4 and 24 ÷ 8 = 3, both exact, so 24 is a common multiple. Then check that no smaller number on the list works.
Multiples, common multiples and the lowest one
The multiples of a number are the results of multiplying it by 1, 2, 3, 4 and so on, so they are the numbers in its times table, continued as far as you like. The multiples of 4 are 4, 8, 12, 16, 20, 24. A common multiple of two numbers is any number that is in both lists.
The lists of multiples never stop, so two numbers have infinitely many common multiples (for 6 and 8: 24, 48, 72 and so on). The lowest common multiple is simply the smallest of them. It is used wherever two things need to line up, most often when adding fractions with different bottom numbers.
Worked example: the LCM of 6 and 8, two ways
Listing method. Multiples of 8: 8, 16, 24, 32. Test each against 6: 8 ÷ 6 and 16 ÷ 6 do not come out exactly, but 24 ÷ 6 = 4 does. So the LCM of 6 and 8 is 24.
Prime factor method (useful for bigger numbers). 6 = 2 × 3 and 8 = 2 × 2 × 2. Take each prime factor the greatest number of times it appears in either number: three 2s (from 8) and one 3 (from 6). Multiply: 2 × 2 × 2 × 3 = 24. Same answer, and it still works for numbers like 36 and 48, where writing out long lists is slow.
The usual mix-ups: LCM versus greatest common factor, and 6 × 8
A multiple is bigger than (or equal to) the number; a factor is smaller than (or equal to) it. The LCM of 6 and 8 is 24, a big number. The greatest common factor of 6 and 8 is 2, a small one. If an answer to an LCM question is smaller than one of the starting numbers, the child has found a factor, not a multiple.
The second mix-up is multiplying the two numbers together. 6 × 8 = 48 is a common multiple, but it is not the lowest one, because 24 also works. Multiplying always gives a common multiple, and it only gives the lowest one when the numbers share no factor other than 1 (for example 4 and 9, where the LCM is 36).
Signs it’s time for outside help
When home help has done what it can
- Cannot continue a times table past 10 × 10 by skip-counting.
- Confuses "multiple" and "factor", or gives a smaller number for an LCM question.
- Always multiplies the two numbers together and does not check for a smaller match.
- Stalls on adding fractions with different bottom numbers.
- Can list multiples but cannot say what the answer means.
Questions parents ask
FAQ
What age do children learn common multiples and the LCM?
Multiples appear from about age 8 or 9 alongside times tables, and the lowest common multiple is usually taught around ages 10–12 (US Grades 5–6, England Years 5–6, Australian Years 5–6), depending on the school.
What is the difference between LCM and "least common multiple"?
Nothing. They are two names for the same thing. "Lowest common multiple" is more common in the UK and Australia and "least common multiple" in the US.
Do I need prime factorisation to find the LCM?
Not for small numbers. Listing multiples is fine for numbers like 6 and 8. Prime factors help when the numbers are larger and the lists get long, so it is worth learning both once the idea is clear.
Why does the LCM matter for fractions?
To add 1/6 and 1/8, both fractions need the same bottom number. The lowest common multiple of 6 and 8, which is 24, is the smallest bottom number that works for both: 4/24 + 3/24 = 7/24.
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