What is the Least Common Multiple of 2100 and 2114?

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 2114 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 2114, than apply into the LCM equation.

GCF(2100,2114) = 14
LCM(2100,2114) = ( 2100 × 2114) / 14
LCM(2100,2114) = 4439400 / 14
LCM(2100,2114) = 317100

Least Common Multiple (LCM) of 2100 and 2114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2100 and 2114. First we will calculate the prime factors of 2100 and 2114.

Prime Factorization of 2100

Prime Factorization of 2114

Now multiplying the highest exponent prime factors to calculate the LCM of 2100 and 2114.

LCM(2100,2114) = 2² × 3¹ × 5² × 7¹ × 151¹
LCM(2100,2114) = 317100