What is the Least Common Multiple of 2180 and 2200?

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 2180 and 2200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2180 and 2200, than apply into the LCM equation.

GCF(2180,2200) = 20
LCM(2180,2200) = ( 2180 × 2200) / 20
LCM(2180,2200) = 4796000 / 20
LCM(2180,2200) = 239800

Least Common Multiple (LCM) of 2180 and 2200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2180 and 2200. First we will calculate the prime factors of 2180 and 2200.

Prime Factorization of 2180

Prime Factorization of 2200

Now multiplying the highest exponent prime factors to calculate the LCM of 2180 and 2200.

LCM(2180,2200) = 2³ × 5² × 109¹ × 11¹
LCM(2180,2200) = 239800