What is the Least Common Multiple of 2112 and 2130?

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 2130 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 2130, than apply into the LCM equation.

GCF(2112,2130) = 6
LCM(2112,2130) = ( 2112 × 2130) / 6
LCM(2112,2130) = 4498560 / 6
LCM(2112,2130) = 749760

Least Common Multiple (LCM) of 2112 and 2130 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2112 and 2130. First we will calculate the prime factors of 2112 and 2130.

Prime Factorization of 2112

Prime Factorization of 2130

Now multiplying the highest exponent prime factors to calculate the LCM of 2112 and 2130.

LCM(2112,2130) = 2⁶ × 3¹ × 11¹ × 5¹ × 71¹
LCM(2112,2130) = 749760