What is the Least Common Multiple of 480 and 493?

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 480 and 493 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 480 and 493, than apply into the LCM equation.

GCF(480,493) = 1
LCM(480,493) = ( 480 × 493) / 1
LCM(480,493) = 236640 / 1
LCM(480,493) = 236640

Least Common Multiple (LCM) of 480 and 493 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 480 and 493. First we will calculate the prime factors of 480 and 493.

Prime Factorization of 480

Prime Factorization of 493

Now multiplying the highest exponent prime factors to calculate the LCM of 480 and 493.

LCM(480,493) = 2⁵ × 3¹ × 5¹ × 17¹ × 29¹
LCM(480,493) = 236640