What is the Least Common Multiple of 51200 and 51205?

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 51205 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 51205, than apply into the LCM equation.

GCF(51200,51205) = 5
LCM(51200,51205) = ( 51200 × 51205) / 5
LCM(51200,51205) = 2621696000 / 5
LCM(51200,51205) = 524339200

Least Common Multiple (LCM) of 51200 and 51205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51200 and 51205. First we will calculate the prime factors of 51200 and 51205.

Prime Factorization of 51200

Prime Factorization of 51205

Now multiplying the highest exponent prime factors to calculate the LCM of 51200 and 51205.

LCM(51200,51205) = 2¹¹ × 5² × 7² × 11¹ × 19¹
LCM(51200,51205) = 524339200