What is the LCM of 10 and 14?
LCM, or Lowest Common Multiple, is the number which is both a multiple of 10 and 14 and is the first number that is.
Many students will look at the two numbers, in this case 10 and 14 and say: "If I multiply 10 and 14, I'll get 140 and that is for sure a multiple of 10 and 14 and so I'll just use that."
And it is true that 140 is a multiple of 10 and 14. But it isn't the lowest. So let's find the lowest.
When I do these, I like to break the numbers in question down to their prime factors:
For 10, the prime factors are 5 and 2 - our LCM will need a 5 and a 2
For 14, the prime factors are 7 and 2 - our LCM will need a 7 and a 2
So we'll need a 2, a 5, and a 7 to make our LCM:
And we can check this by saying:
The first attempt we made, with 140, wasn't the lowest because it had an extra 2 that wasn't needed:
Consider the prime factors of 10 and 14.
Hence the factors of the lowest common multiple must be