How do you find the least common multiple with the factor tree/prime factorization?

Question

How do you find the least common multiple with the factor tree/prime factorization?

Answer 1

Find LCM of 34,49. and 56

34 = 2*17

49 = 7*7

56 = 2*2*2*7

So LCM = 8*49*17= 6664

Answer 2

Factorize the numbers, then in the least common multiple all prime factors of the factorized numbers must be factors of the LCM, and the LCM doesn't have other factors. Now, you have to see the power of each prime factor of the LCM. For every prime factor, look at its power in the numbers and take the biggest one for the LCM. That's it :)

I'll show you an example because this doesn't look very clear:

Take the numbers 12, 45, 64 and 200

12 = 2^2 *3

45 = 3^2 *5

64 = 2^6

200 = 2^3 * 5^2

So, LCM(12, 45, 64, 200) = 2^6 * 3^2 * 5^2

because the highest power of 2 in the numbers is 6th, of 3 is second, and of 5 is second

Hope this helps :)