GCF and LCM of 252, 420, and 180
252: 2,2,3,3,7
420: 2,2,3,5,7
180: 2,2,3,3,5
GCF is 12 and I think LCM is 1260?
Can you please tell me if I'm right?
yes, two 2s and a 3
yes, 420 * 3
To find the greatest common factor (GCF) and least common multiple (LCM) of numbers, you can use prime factorization.
To find the GCF, you need to find the highest power of each common prime factor among the given numbers. For example:
The prime factorization of 252 is 2 x 2 x 3 x 3 x 7.
The prime factorization of 420 is 2 x 2 x 3 x 5 x 7.
The prime factorization of 180 is 2 x 2 x 3 x 3 x 5.
From the prime factorizations, we can see that the common prime factors among the three numbers are 2, 3, and 7. Taking the highest power of each common factor, we get:
2^2, 3^2, 7^1
Multiplying these together gives us the GCF:
GCF = 2^2 x 3^2 x 7^1 = 4 x 9 x 7 = 252
So, the GCF of 252, 420, and 180 is 252.
To find the LCM, you need to find the product of each prime factor raised to the highest power it appears in any of the given numbers. In this case:
2^2, 3^2, 5^1, 7^1
Multiplying these together gives us the LCM:
LCM = 2^2 x 3^2 x 5^1 x 7^1 = 4 x 9 x 5 x 7 = 1260
So, yes, you are correct! The GCF is 252 and the LCM is 1260.