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how to find to common multiples of large numbers

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2 Answers

Hi, Thinath.

Multiplying numbers together gives you a common multiple. If you want to find the least common multiple, though, you can use the prime factorization method. For example, let's find the LCM of 200 and 315.

Write both numbers as the product of their prime factors:

200 = 23 x 52

315 = 32 x 5 x 7

The least common multiple is the product of the higher degree of each unique factor. In this example, all the factors are unique except the 5. We'll use 52 since it is the higher degree.

LCM = 23 x 32 x 52 x 7 = 12,600

Hope this helps!

First of all, if x and y are any two positive integers, then LCM(x,y) = xy / GCD(x,y)

Therefore, to find LCM(x,y), we need to find GCD(x,y) first.

GCD(x,y) can be found using Euclids algorithm:

If x = ay+b, then GCD(x,y) = GCD(y,b). Here is an example.

Say that x = 78 and y = 60. Then

  GCD(78,60)

= GCD(60,18)

= GCD(18,6)

= GCD(6,0)

= 6

So LCM(78,60) = 78*60/6 = 780