What is the Least Common Multiple of 2138 and 2158?

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 2138 and 2158 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2138 and 2158, than apply into the LCM equation.

GCF(2138,2158) = 2
LCM(2138,2158) = ( 2138 × 2158) / 2
LCM(2138,2158) = 4613804 / 2
LCM(2138,2158) = 2306902

Least Common Multiple (LCM) of 2138 and 2158 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2138 and 2158. First we will calculate the prime factors of 2138 and 2158.

Prime Factorization of 2138

Prime Factorization of 2158

Now multiplying the highest exponent prime factors to calculate the LCM of 2138 and 2158.

LCM(2138,2158) = 2¹ × 1069¹ × 13¹ × 83¹
LCM(2138,2158) = 2306902