The product of two numbers is 180. The LCM of the two numbers is 60. What is the GCF of the two numbers? How do you know?
The LCM of two numbers is 60. If the product of the two numbers is 180, find their HCF
nice question
the possible 2 numbers were
1 180
2 90
3 60
4 45
5 36
6 30
9 20
12 15
of those only the 3 60 pair has a LCM of 60
the GCF of the pair is 3
To find the greatest common factor (GCF) of two numbers, we need to determine the largest number that can evenly divide both numbers. We are given that the product of the two numbers is 180 and the least common multiple (LCM) is 60.
To find the GCF, we first need to determine the prime factorization of both numbers. Let's call the two numbers "a" and "b."
The prime factorization of the product 180 can be written as: 2^2 * 3^2 * 5.
The prime factorization of the LCM 60 can be written as: 2^2 * 3 * 5.
Now we need to find the common prime factors between these two factorizations. The common prime factors are 2, 3, and 5.
To determine the GCF, we multiply together these common prime factors with their lowest exponents. In this case, 2^2 * 3 * 5, which equals 60.
Therefore, the GCF of the two numbers is 60. We know this is true because the GCF is the highest possible factor that both numbers share, and it can be obtained by multiplying the common prime factors with their lowest exponents.
We know that,
LCM(a,b) X HCF(a,b) = Product of a and b
Therefore, 60 X HCF(a,b) = 180
= HCF(a,b) = 3
Therefore HCF of the two numbers is 3
Hope it helped =)