What is the Least Common Multiple of 51200 and 51210?

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 51200 and 51210 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51200 and 51210, than apply into the LCM equation.

GCF(51200,51210) = 10
LCM(51200,51210) = ( 51200 × 51210) / 10
LCM(51200,51210) = 2621952000 / 10
LCM(51200,51210) = 262195200

Least Common Multiple (LCM) of 51200 and 51210 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51200 and 51210. First we will calculate the prime factors of 51200 and 51210.

Prime Factorization of 51200

Prime Factorization of 51210

Now multiplying the highest exponent prime factors to calculate the LCM of 51200 and 51210.

LCM(51200,51210) = 2¹¹ × 5² × 3² × 569¹
LCM(51200,51210) = 262195200