What is the Least Common Multiple of 54735 and 54750?

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 54735 and 54750 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54735 and 54750, than apply into the LCM equation.

GCF(54735,54750) = 15
LCM(54735,54750) = ( 54735 × 54750) / 15
LCM(54735,54750) = 2996741250 / 15
LCM(54735,54750) = 199782750

Least Common Multiple (LCM) of 54735 and 54750 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54735 and 54750. First we will calculate the prime factors of 54735 and 54750.

Prime Factorization of 54735

Prime Factorization of 54750

Now multiplying the highest exponent prime factors to calculate the LCM of 54735 and 54750.

LCM(54735,54750) = 3¹ × 5³ × 41¹ × 89¹ × 2¹ × 73¹
LCM(54735,54750) = 199782750