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