I know that LCM is all the numbers with the largest exponents, but I cant remember GCF. Is GCF only the numbers in common with the smallest exponents, or is it ALL numbers with smallest exponents?

Question

anonymous · Answer

only primes in common. example:
gcd(150, 40)
150 = 15*10 = 3*5*5*2 = 2*3*5^2
40 = 4*10 = 2^3*5
the gcd would only have a 2*5, so the gcd is 10.

anonymous · Answer

LCM = Leas Common Multiple
GCF = Greatest Common Factor

anonymous · Answer

Yes thank you I understand what the letters stand for, but my question is when it has too do with exponents. With GCF I know when you list out all the factors of two numbers you to find the GCF you only take the smallest exponents, but do you take the smallest exponents from all the numbers, or only the smallest exponents that the two beginning numbers have in common?

anonymous · Answer

only what they have in common.  If one number has 17^2 as a prime factor, and the other doesnt, you wouldnt want to put 17^2 in the gcd. just look at the primes in common, and take the lowest exponent.

anonymous · Answer

LCM in 12 and 8 would be:
8 = 8, 16, 24, 32, 40, etc.
12 = 12, 24, 36, 48, etc.
LCM = 24

GCF is 12 and 8 would be:
8 = 2*2*2
12 = 2*2*3
GCF = 2*2 = "4"

anonymous · Answer

Thank you, this is what I thought but I wanted too be completely sure!