What is the Least Common Multiple of 53460 and 53475?

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 53460 and 53475 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 53460 and 53475, than apply into the LCM equation.

GCF(53460,53475) = 15
LCM(53460,53475) = ( 53460 × 53475) / 15
LCM(53460,53475) = 2858773500 / 15
LCM(53460,53475) = 190584900

Least Common Multiple (LCM) of 53460 and 53475 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 53460 and 53475. First we will calculate the prime factors of 53460 and 53475.

Prime Factorization of 53460

Prime Factorization of 53475

Now multiplying the highest exponent prime factors to calculate the LCM of 53460 and 53475.

LCM(53460,53475) = 2² × 3⁵ × 5² × 11¹ × 23¹ × 31¹
LCM(53460,53475) = 190584900