Question

I need an example for my homework

Answer 1

There are at least a couple of methods you can use to find the GCF. One is to simply list the prime factors, then pick all the ones that are common and multiply those together.

1) 18 = 2·3·3

...20 = 2·2·5

The only factor appearing on both lists is 2, so GCF(18, 20) = 2.

The LCM is the product of the numbers divided by the GCF. Here, that is

... 18 × 20 ÷ 2 = 180

LCM(18, 20) = 180

2) The only prime factor of 2 is 2. The only prime factor of 3 is 3 (twice), so 2 and 9 have no common factors except 1. GCF(2, 9) = 1.

LCM(2, 9) = 2 × 9 ÷ 1 = 18

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Another method you can use to find the GCF is Euclid's Algorithm. Divide the larger number by the smaller and examine the remainder. If the remainder is zero (0), the smaller number is the GCF. If not, find the GCF of the smaller number and the remainder.

For problem 1 above, this looks like

... 20/18 = 1 r 2 . . . . 2 is not zero, so now we're looking for the GCF of 2 and 18

... 18/2 = 9 r 0 . . . . . the remainder is 0, so 2 is the GCF