What is the Least Common Multiple of 6132 and 6144?

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 6132 and 6144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6132 and 6144, than apply into the LCM equation.

GCF(6132,6144) = 12
LCM(6132,6144) = ( 6132 × 6144) / 12
LCM(6132,6144) = 37675008 / 12
LCM(6132,6144) = 3139584

Least Common Multiple (LCM) of 6132 and 6144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6132 and 6144. First we will calculate the prime factors of 6132 and 6144.

Prime Factorization of 6132

Prime Factorization of 6144

Now multiplying the highest exponent prime factors to calculate the LCM of 6132 and 6144.

LCM(6132,6144) = 2¹¹ × 3¹ × 7¹ × 73¹
LCM(6132,6144) = 3139584