What is the Least Common Multiple of 465 and 480?

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 465 and 480 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 465 and 480, than apply into the LCM equation.

GCF(465,480) = 15
LCM(465,480) = ( 465 × 480) / 15
LCM(465,480) = 223200 / 15
LCM(465,480) = 14880

Least Common Multiple (LCM) of 465 and 480 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 465 and 480. First we will calculate the prime factors of 465 and 480.

Prime Factorization of 465

Prime Factorization of 480

Now multiplying the highest exponent prime factors to calculate the LCM of 465 and 480.

LCM(465,480) = 3¹ × 5¹ × 31¹ × 2⁵
LCM(465,480) = 14880