Lowest common multiple

Hello, and welcome to Myriora Maths! Two buses leave the bus station at eight o'clock. The red bus comes back every four minutes. The blue bus comes back every six minutes. When will they both be back at the same time? Let's find out!

Let's draw a timeline. The red bus is back at four, eight, twelve, sixteen, twenty and twenty-four minutes. The blue bus is back at six, twelve, eighteen and twenty-four. They meet at twelve minutes past eight, and again at twenty-four minutes past!

Twelve is the first time they meet. It's called the lowest common multiple, or L C M: the smallest number that's in both times tables.

You can find it with prime factors too. Four is two times two. Six is two times three. The L C M needs everything that each number needs: two twos for the four, and a three for the six. Two times two times three is twelve.

Why not just multiply? Four times six is twenty-four. That's a common multiple, but it's not the lowest. Four and six share a two, so multiplying them counts that two twice. That's why twenty-four is double the answer.

Try eight and twelve. Eight is two times two times two. Twelve is two times two times three. Take three twos for the eight, and a three for the twelve. Two times two times two times three is twenty-four.

Here's a question that catches lots of people. What is the L C M of four and six? Some people just multiply, and say twenty-four. It is a common multiple, but it's not the lowest one. The lowest is twelve!

Your turn! What is the lowest common multiple of six and eight? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Count in eights: eight, sixteen, twenty-four. Twenty-four is in the six times table too: it's four sixes! So the L C M is twenty-four.

Quick review. The L C M is the smallest number in both times tables. You can list the multiples until they match. Or take every prime factor that each number needs. Just multiplying gives a common multiple, but often not the lowest. See you next time!