What is the Least Common Multiple of 240 and 249?

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 240 and 249 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 240 and 249, than apply into the LCM equation.

GCF(240,249) = 3
LCM(240,249) = ( 240 × 249) / 3
LCM(240,249) = 59760 / 3
LCM(240,249) = 19920

Least Common Multiple (LCM) of 240 and 249 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 240 and 249. First we will calculate the prime factors of 240 and 249.

Prime Factorization of 240

Prime Factorization of 249

Now multiplying the highest exponent prime factors to calculate the LCM of 240 and 249.

LCM(240,249) = 2⁴ × 3¹ × 5¹ × 83¹
LCM(240,249) = 19920