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Lowest Common Multiple (LCM)

In one line: The lowest common multiple (LCM) of two or more numbers is the smallest number, bigger than zero, that is in all of their times tables.

Why it works

A multiple is what you get when you multiply a number by 1, 2, 3 and so on. For example, the multiples of 4 are 4, 8, 12, 16 and so on. A common multiple is a number that is in the times tables of every number you are looking at, and the lowest one is the smallest of these. The LCM helps you add and subtract fractions, because it gives the smallest shared bottom number (the common denominator). It also solves everyday puzzles, such as working out when two buses that leave at different intervals will next leave together.

Think of it like: Imagine two friends hopping along a number line that starts at 0. One friend always jumps 6 spaces and the other always jumps 8 spaces. Each friend lands on their own times table: 6, 12, 18, 24… and 8, 16, 24… The first number where both friends land on the same spot is 24. That meeting spot is the lowest common multiple. (Where this breaks: The hopping picture works well for two small numbers, but it gets slow for big numbers or for three or more numbers, where listing every landing spot takes a long time. For those, it is quicker to use prime factors (breaking each number into a product of prime numbers, which are numbers with exactly two factors: 1 and themselves).)

Worked example

Bus A leaves the station every 6 minutes and Bus B leaves every 8 minutes. They both leave together at 9:00. When will they next leave together?

  1. Spot that this is an LCM question: we need the smallest time that is in both the 6 times table and the 8 times table.
  2. List multiples of the bigger number, 8: 8, 16, 24, 32…
  3. Check each one to see if 6 divides into it exactly: 8 no, 16 no, 24 yes (6 × 4 = 24).
  4. So the LCM of 6 and 8 is 24.
  5. Add 24 minutes to 9:00 to get the time.

Answer: The LCM of 6 and 8 is 24, so the buses next leave together at 9:24.

Common mistakes

  • Just multiplying the two numbers together (6 × 8 = 48) gives a common multiple but not always the lowest one, so always check smaller multiples of the bigger number first.
  • Mixing up the LCM with the highest common factor (the biggest number that divides into both) gives an answer that is too small, so remember a multiple is at least as big as the number itself.
  • Stopping at a number that is in only one of the times tables is a slip, so check that every number divides exactly into your answer.
  • Giving 0 as the answer is wrong because we only count multiples bigger than zero, so start your lists at the number itself.

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What is the lowest common multiple of 4 and 6?

Questions parents ask

What year do kids learn lowest common multiple?

Children usually meet common multiples around Year 5 and Year 6 in the UK and Australia, with the term 'lowest common multiple' becoming more common by Year 6 to Year 7. In the US it is usually taught in Grade 6. It builds directly on knowing times tables well.

What is the difference between LCM and HCF?

The lowest common multiple is the smallest number that all the numbers divide into, so it is usually bigger than the numbers. The highest common factor (also called greatest common factor) is the biggest number that divides into all of them, so it is usually smaller. For 6 and 8, the LCM is 24 and the HCF is 2.

How can I help my child with lowest common multiple at home?

Practise times tables first, because finding the LCM is much easier when multiples come quickly. Then try real puzzles, like 'if one tap drips every 3 seconds and another every 5 seconds, when do they drip together?' Encourage your child to list multiples of the bigger number and check each one.

Why do kids need the lowest common multiple for fractions?

To add or subtract fractions like 1/4 + 1/6, the bottom numbers must match. The LCM of 4 and 6 is 12, so both fractions can be changed into twelfths (3/12 + 2/12 = 5/12). Using the LCM keeps the numbers as small as possible, which means less simplifying at the end.