What is the Least Common Multiple of 2112 and 2132?

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 2112 and 2132 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2112 and 2132, than apply into the LCM equation.

GCF(2112,2132) = 4
LCM(2112,2132) = ( 2112 × 2132) / 4
LCM(2112,2132) = 4502784 / 4
LCM(2112,2132) = 1125696

Least Common Multiple (LCM) of 2112 and 2132 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2112 and 2132. First we will calculate the prime factors of 2112 and 2132.

Prime Factorization of 2112

Prime Factorization of 2132

Now multiplying the highest exponent prime factors to calculate the LCM of 2112 and 2132.

LCM(2112,2132) = 2⁶ × 3¹ × 11¹ × 13¹ × 41¹
LCM(2112,2132) = 1125696