What is the Least Common Multiple of 456 and 460?

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 456 and 460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 456 and 460, than apply into the LCM equation.

GCF(456,460) = 4
LCM(456,460) = ( 456 × 460) / 4
LCM(456,460) = 209760 / 4
LCM(456,460) = 52440

Least Common Multiple (LCM) of 456 and 460 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 456 and 460. First we will calculate the prime factors of 456 and 460.

Prime Factorization of 456

Prime Factorization of 460

Now multiplying the highest exponent prime factors to calculate the LCM of 456 and 460.

LCM(456,460) = 2³ × 3¹ × 19¹ × 5¹ × 23¹
LCM(456,460) = 52440