What is the Least Common Multiple of 2460 and 2475?

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 2460 and 2475 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2460 and 2475, than apply into the LCM equation.

GCF(2460,2475) = 15
LCM(2460,2475) = ( 2460 × 2475) / 15
LCM(2460,2475) = 6088500 / 15
LCM(2460,2475) = 405900

Least Common Multiple (LCM) of 2460 and 2475 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2460 and 2475. First we will calculate the prime factors of 2460 and 2475.

Prime Factorization of 2460

Prime Factorization of 2475

Now multiplying the highest exponent prime factors to calculate the LCM of 2460 and 2475.

LCM(2460,2475) = 2² × 3² × 5² × 41¹ × 11¹
LCM(2460,2475) = 405900