What is the least common multiple of 10 and 12 and15?

Answer 1

The best way to do this is to find the LCM of the highest 2 numbers (a) and (b) and then work with the last (c) relative to the LCM of (a) and (b).

LCM(a,b) = (ab)/(gcf(a,b))

12 factors to [2 2 3]

15 factors to [3 5]

common factor is [3]

LCM(12,15) = (12)(15)/3 = 60

Happily, 10 is a factor of 60, so 60 is the LCM(10,60) and you are done here.

60 is the answer.◄

If you want to work it all the way out...

10 factors to [2 5]

60 factors to [2 2 3 5]

common factors are [2 5]

LCM(10,60) = (10)(60)/(10) = 60

If you follow the formula, it will always work.