Answer:
\(\text{Product of two numbers}=GCF\times LCM\)
Step-by-step 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
\(\text{Product of two numbers}=GCF\times LCM\)
Factor the numbers 12 and 20,
\(12=2\times 2\times 3\)
\(20=2\times 2\times 5\)
The GCF of the numbers is
\(GCF(12,20)=2\times 2\)
\(GCF(12,20)=4\)
The LCM of the numbers is
\(LCM(12,20)=60\)
Now we verify the relationship,
LHS, \(\text{Product of two numbers}=12\times 20\)
\(\text{Product of two numbers}=240\)
RHS, \(GCF\times LCM=4\times 60\)
\(GCF\times LCM=240\)
LHS=RHS
