Question

If a = 2^3 x 3^7 x 5^3 x 11^4 and b = 2^2 x 3^9 x 7^2 x 11 x 13, find the following: A. GCF (a, b) B. LCM (a, b)

Answer 1

A. GCF(a,b) =
`2^2 * 3^7 * 11`

B. LCM(a,b) =
`2^3 * 3^9 * 5^3 * 7^2 * 11^4 * 13`

Explanation:

The GCF of two or more integers is their greatest common factor. In order to find it, you must factorise them first and then do the product of the factors that appear in all the factorisations, with their least exponent.

Hence, the GCF of
`a` and
`b` is
`2^2 * 3^7 * 11`.

The LCM of two or more integers is their least common multiple. In order to find it, you must factorise them first and then do the product of the multiples that appear in one or all the factorisations, with their greatest exponent.

Hence, the LCM of
`a` and
`b` is
`2^3 * 3^9 * 5^3 * 7^2 * 11^4 * 13`