What is the Least Common Multiple of 480 and 489?

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 489 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 489, than apply into the LCM equation.

GCF(480,489) = 3
LCM(480,489) = ( 480 × 489) / 3
LCM(480,489) = 234720 / 3
LCM(480,489) = 78240

Least Common Multiple (LCM) of 480 and 489 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 480 and 489. First we will calculate the prime factors of 480 and 489.

Prime Factorization of 480

Prime Factorization of 489

Now multiplying the highest exponent prime factors to calculate the LCM of 480 and 489.

LCM(480,489) = 2⁵ × 3¹ × 5¹ × 163¹
LCM(480,489) = 78240