What is the Least Common Multiple of 54144 and 54164?

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 54144 and 54164 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54144 and 54164, than apply into the LCM equation.

GCF(54144,54164) = 4
LCM(54144,54164) = ( 54144 × 54164) / 4
LCM(54144,54164) = 2932655616 / 4
LCM(54144,54164) = 733163904

Least Common Multiple (LCM) of 54144 and 54164 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54144 and 54164. First we will calculate the prime factors of 54144 and 54164.

Prime Factorization of 54144

Prime Factorization of 54164

Now multiplying the highest exponent prime factors to calculate the LCM of 54144 and 54164.

LCM(54144,54164) = 2⁷ × 3² × 47¹ × 11¹ × 1231¹
LCM(54144,54164) = 733163904