What is the Least Common Multiple of 2200 and 2208?

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 2208 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 2208, than apply into the LCM equation.

GCF(2200,2208) = 8
LCM(2200,2208) = ( 2200 × 2208) / 8
LCM(2200,2208) = 4857600 / 8
LCM(2200,2208) = 607200

Least Common Multiple (LCM) of 2200 and 2208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2200 and 2208. First we will calculate the prime factors of 2200 and 2208.

Prime Factorization of 2200

Prime Factorization of 2208

Now multiplying the highest exponent prime factors to calculate the LCM of 2200 and 2208.

LCM(2200,2208) = 2⁵ × 5² × 11¹ × 3¹ × 23¹
LCM(2200,2208) = 607200