What is the Least Common Multiple of 2100 and 2112?

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 2100 and 2112 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2100 and 2112, than apply into the LCM equation.

GCF(2100,2112) = 12
LCM(2100,2112) = ( 2100 × 2112) / 12
LCM(2100,2112) = 4435200 / 12
LCM(2100,2112) = 369600

Least Common Multiple (LCM) of 2100 and 2112 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2112. First we will calculate the prime factors of 2100 and 2112.

Prime Factorization of 2100

Prime Factorization of 2112

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2112.

LCM(2100,2112) = 2⁶ × 3¹ × 5² × 7¹ × 11¹
LCM(2100,2112) = 369600