What is the Least Common Multiple of 2120 and 2138?

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 2120 and 2138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2120 and 2138, than apply into the LCM equation.

GCF(2120,2138) = 2
LCM(2120,2138) = ( 2120 × 2138) / 2
LCM(2120,2138) = 4532560 / 2
LCM(2120,2138) = 2266280

Least Common Multiple (LCM) of 2120 and 2138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2120 and 2138. First we will calculate the prime factors of 2120 and 2138.

Prime Factorization of 2120

Prime Factorization of 2138

Now multiplying the highest exponent prime factors to calculate the LCM of 2120 and 2138.

LCM(2120,2138) = 2³ × 5¹ × 53¹ × 1069¹
LCM(2120,2138) = 2266280