What is the Least Common Multiple of 54750 and 54768?

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 54750 and 54768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54750 and 54768, than apply into the LCM equation.

GCF(54750,54768) = 6
LCM(54750,54768) = ( 54750 × 54768) / 6
LCM(54750,54768) = 2998548000 / 6
LCM(54750,54768) = 499758000

Least Common Multiple (LCM) of 54750 and 54768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54750 and 54768. First we will calculate the prime factors of 54750 and 54768.

Prime Factorization of 54750

Prime Factorization of 54768

Now multiplying the highest exponent prime factors to calculate the LCM of 54750 and 54768.

LCM(54750,54768) = 2⁴ × 3¹ × 5³ × 73¹ × 7¹ × 163¹
LCM(54750,54768) = 499758000