What is the Least Common Multiple of 30240 and 30249?

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 30240 and 30249 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30240 and 30249, than apply into the LCM equation.

GCF(30240,30249) = 9
LCM(30240,30249) = ( 30240 × 30249) / 9
LCM(30240,30249) = 914729760 / 9
LCM(30240,30249) = 101636640

Least Common Multiple (LCM) of 30240 and 30249 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30240 and 30249. First we will calculate the prime factors of 30240 and 30249.

Prime Factorization of 30240

Prime Factorization of 30249

Now multiplying the highest exponent prime factors to calculate the LCM of 30240 and 30249.

LCM(30240,30249) = 2⁵ × 3³ × 5¹ × 7¹ × 3361¹
LCM(30240,30249) = 101636640