What is the Least Common Multiple of 54750 and 54765?

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 54765 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 54765, than apply into the LCM equation.

GCF(54750,54765) = 15
LCM(54750,54765) = ( 54750 × 54765) / 15
LCM(54750,54765) = 2998383750 / 15
LCM(54750,54765) = 199892250

Least Common Multiple (LCM) of 54750 and 54765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54750 and 54765. First we will calculate the prime factors of 54750 and 54765.

Prime Factorization of 54750

Prime Factorization of 54765

Now multiplying the highest exponent prime factors to calculate the LCM of 54750 and 54765.

LCM(54750,54765) = 2¹ × 3² × 5³ × 73¹ × 1217¹
LCM(54750,54765) = 199892250