What is the Least Common Multiple of 2200 and 2205?

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 2200 and 2205 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2200 and 2205, than apply into the LCM equation.

GCF(2200,2205) = 5
LCM(2200,2205) = ( 2200 × 2205) / 5
LCM(2200,2205) = 4851000 / 5
LCM(2200,2205) = 970200

Least Common Multiple (LCM) of 2200 and 2205 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2200 and 2205. First we will calculate the prime factors of 2200 and 2205.

Prime Factorization of 2200

Prime Factorization of 2205

Now multiplying the highest exponent prime factors to calculate the LCM of 2200 and 2205.

LCM(2200,2205) = 2³ × 5² × 11¹ × 3² × 7²
LCM(2200,2205) = 970200