What is the Least Common Multiple of 249 and 264?

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 249 and 264 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 249 and 264, than apply into the LCM equation.

GCF(249,264) = 3
LCM(249,264) = ( 249 × 264) / 3
LCM(249,264) = 65736 / 3
LCM(249,264) = 21912

Least Common Multiple (LCM) of 249 and 264 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 249 and 264. First we will calculate the prime factors of 249 and 264.

Prime Factorization of 249

Prime Factorization of 264

Now multiplying the highest exponent prime factors to calculate the LCM of 249 and 264.

LCM(249,264) = 3¹ × 83¹ × 2³ × 11¹
LCM(249,264) = 21912