Question

what is the relationship of the product of 12 and 20 to the product of the gcf and the Lcm of the two numbers?

Answer 1

I hope this helps you

Answer 2

`\text{Product of two numbers}=GCF* LCM`

Explanation:

Given : Number 12 and 20.

To find : What is the relationship of the product of numbers to the product of the GCF and the LCM of the two numbers?

Solution :

The relationship of the product of numbers to the product of the GCF and the LCM of the two numbers is

`\text{Product of two numbers}=GCF* LCM`

Factor the numbers 12 and 20,

`12=2* 2* 3`

`20=2* 2* 5`

The GCF of the numbers is

`GCF(12,20)=2* 2`

`GCF(12,20)=4`

The LCM of the numbers is

`LCM(12,20)=60`

Now we verify the relationship,

LHS,
`\text{Product of two numbers}=12* 20`

`\text{Product of two numbers}=240`

RHS,
`GCF* LCM=4* 60`

`GCF* LCM=240`

LHS=RHS