What is the Least Common Multiple of 30264 and 30272?

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 30264 and 30272 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30264 and 30272, than apply into the LCM equation.

GCF(30264,30272) = 8
LCM(30264,30272) = ( 30264 × 30272) / 8
LCM(30264,30272) = 916151808 / 8
LCM(30264,30272) = 114518976

Least Common Multiple (LCM) of 30264 and 30272 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30264 and 30272. First we will calculate the prime factors of 30264 and 30272.

Prime Factorization of 30264

Prime Factorization of 30272

Now multiplying the highest exponent prime factors to calculate the LCM of 30264 and 30272.

LCM(30264,30272) = 2⁶ × 3¹ × 13¹ × 97¹ × 11¹ × 43¹
LCM(30264,30272) = 114518976