What is the Least Common Multiple of 57000 and 57008?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 57000 and 57008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 57000 and 57008, than apply into the LCM equation.

GCF(57000,57008) = 8
LCM(57000,57008) = ( 57000 × 57008) / 8
LCM(57000,57008) = 3249456000 / 8
LCM(57000,57008) = 406182000

Least Common Multiple (LCM) of 57000 and 57008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 57000 and 57008. First we will calculate the prime factors of 57000 and 57008.

Prime Factorization of 57000

Prime Factorization of 57008

Now multiplying the highest exponent prime factors to calculate the LCM of 57000 and 57008.

LCM(57000,57008) = 2⁴ × 3¹ × 5³ × 19¹ × 7¹ × 509¹
LCM(57000,57008) = 406182000