The product of the GCF and LCM of two numbers is 12. Give one possible pair of values for the two numbers
the LCM ≥ GCF
So the only cases to get a product of 12 is:
12 1
6 2
4 3
suppose we have a LCM of 12 and a GCF of 1
how about 12, 1 coming from 3,4
checking:
so the number pair (3,4)
has a LCF of 1 , and a HCM of 12,
product is (1)(12) = 12
looks good!
does 6,2 work?
LCM = 6 ,
GCF = 2 ----> can't think of any
can you think of anything that will make
LCM = 4
GCF = 3 ?
4 and 3
Thanks
Thanks
For everything
thanks it helped me learn how to do it
To find a possible pair of values for the two numbers, we need to understand the relationship between the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of two numbers.
The GCF is the largest number that divides both numbers evenly, while the LCM is the smallest number that is a multiple of both numbers.
Given that the product of the GCF and LCM is 12, we can set up an equation:
GCF * LCM = 12
Now, let's list out some factors and multiples of 12 to identify possible pairs of values. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the multiples of 12 are 12, 24, 36, 48, and so on.
By examining the factors and multiples, we can see that if the GCF is 1 and the LCM is 12, it satisfies the given condition since 1 multiplied by 12 equals 12. Therefore, a possible pair of values for the two numbers is (1, 12).
Keep in mind that there may be other pairs of values that satisfy the condition, but (1, 12) is one possible solution.