What is the Least Common Multiple of 30144 and 30156?

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 30144 and 30156 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30144 and 30156, than apply into the LCM equation.

GCF(30144,30156) = 12
LCM(30144,30156) = ( 30144 × 30156) / 12
LCM(30144,30156) = 909022464 / 12
LCM(30144,30156) = 75751872

Least Common Multiple (LCM) of 30144 and 30156 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30144 and 30156. First we will calculate the prime factors of 30144 and 30156.

Prime Factorization of 30144

Prime Factorization of 30156

Now multiplying the highest exponent prime factors to calculate the LCM of 30144 and 30156.

LCM(30144,30156) = 2⁶ × 3¹ × 157¹ × 7¹ × 359¹
LCM(30144,30156) = 75751872