What is the Least Common Multiple of 56985 and 57000?

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 56985 and 57000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 56985 and 57000, than apply into the LCM equation.

GCF(56985,57000) = 15
LCM(56985,57000) = ( 56985 × 57000) / 15
LCM(56985,57000) = 3248145000 / 15
LCM(56985,57000) = 216543000

Least Common Multiple (LCM) of 56985 and 57000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 56985 and 57000. First we will calculate the prime factors of 56985 and 57000.

Prime Factorization of 56985

Prime Factorization of 57000

Now multiplying the highest exponent prime factors to calculate the LCM of 56985 and 57000.

LCM(56985,57000) = 3¹ × 5³ × 29¹ × 131¹ × 2³ × 19¹
LCM(56985,57000) = 216543000