What is the Least Common Multiple of 30048 and 30057?

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 30048 and 30057 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30048 and 30057, than apply into the LCM equation.

GCF(30048,30057) = 3
LCM(30048,30057) = ( 30048 × 30057) / 3
LCM(30048,30057) = 903152736 / 3
LCM(30048,30057) = 301050912

Least Common Multiple (LCM) of 30048 and 30057 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30048 and 30057. First we will calculate the prime factors of 30048 and 30057.

Prime Factorization of 30048

Prime Factorization of 30057

Now multiplying the highest exponent prime factors to calculate the LCM of 30048 and 30057.

LCM(30048,30057) = 2⁵ × 3¹ × 313¹ × 43¹ × 233¹
LCM(30048,30057) = 301050912