Question

Given the GCF or LCM, what else do you know about each pair of numbers?

a) Two numbers have a GCF of 2.
b) Two numbers have an LCM of 2.
c) Two numbers have a GCF of 3.
d) Two numbers have an LCM of 10.

Answer 1

1. LCM is half of given product.
2. GCF is half of given product.
3. LCM is one-third of given product.
4. GCF is one-tenth of given product.

Explanation:

We know that'

GCF × LCM = Product of given number

1. Two numbers have a GCF of 2

= 2 × LCM = Product of given number

LCM = Product of given number / 2

LCM is half of given product.

2. Two numbers have an LCM of 2

= GCF × 2 = Product of given number

GCF = Product of given number / 2

GCF is half of given product.

3. Two numbers have a GCF of 3

= 3 × LCM = Product of given number

LCM = Product of given number / 3

LCM is one-third of given product.

4. Two numbers have an LCM of 10

= GCF × 10 = Product of given number

GCF = Product of given number / 10

GCF is one-tenth of given product.