What is the Least Common Multiple of 2142 and 2149?

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 2142 and 2149 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2142 and 2149, than apply into the LCM equation.

GCF(2142,2149) = 7
LCM(2142,2149) = ( 2142 × 2149) / 7
LCM(2142,2149) = 4603158 / 7
LCM(2142,2149) = 657594

Least Common Multiple (LCM) of 2142 and 2149 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2142 and 2149. First we will calculate the prime factors of 2142 and 2149.

Prime Factorization of 2142

Prime Factorization of 2149

Now multiplying the highest exponent prime factors to calculate the LCM of 2142 and 2149.

LCM(2142,2149) = 2¹ × 3² × 7¹ × 17¹ × 307¹
LCM(2142,2149) = 657594