What is the Least Common Multiple of 2130 and 2142?

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 2130 and 2142 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2130 and 2142, than apply into the LCM equation.

GCF(2130,2142) = 6
LCM(2130,2142) = ( 2130 × 2142) / 6
LCM(2130,2142) = 4562460 / 6
LCM(2130,2142) = 760410

Least Common Multiple (LCM) of 2130 and 2142 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2130 and 2142. First we will calculate the prime factors of 2130 and 2142.

Prime Factorization of 2130

Prime Factorization of 2142

Now multiplying the highest exponent prime factors to calculate the LCM of 2130 and 2142.

LCM(2130,2142) = 2¹ × 3² × 5¹ × 71¹ × 7¹ × 17¹
LCM(2130,2142) = 760410