What is the Least Common Multiple of 12132 and 12144?

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 12132 and 12144 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12132 and 12144, than apply into the LCM equation.

GCF(12132,12144) = 12
LCM(12132,12144) = ( 12132 × 12144) / 12
LCM(12132,12144) = 147331008 / 12
LCM(12132,12144) = 12277584

Least Common Multiple (LCM) of 12132 and 12144 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12132 and 12144. First we will calculate the prime factors of 12132 and 12144.

Prime Factorization of 12132

Prime Factorization of 12144

Now multiplying the highest exponent prime factors to calculate the LCM of 12132 and 12144.

LCM(12132,12144) = 2⁴ × 3² × 337¹ × 11¹ × 23¹
LCM(12132,12144) = 12277584