What is the Least Common Multiple of 1146 and 1152?

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 1146 and 1152 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1146 and 1152, than apply into the LCM equation.

GCF(1146,1152) = 6
LCM(1146,1152) = ( 1146 × 1152) / 6
LCM(1146,1152) = 1320192 / 6
LCM(1146,1152) = 220032

Least Common Multiple (LCM) of 1146 and 1152 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1146 and 1152. First we will calculate the prime factors of 1146 and 1152.

Prime Factorization of 1146

Prime Factorization of 1152

Now multiplying the highest exponent prime factors to calculate the LCM of 1146 and 1152.

LCM(1146,1152) = 2⁷ × 3² × 191¹
LCM(1146,1152) = 220032