What is the Least Common Multiple of 2208 and 2228?

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 2208 and 2228 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2208 and 2228, than apply into the LCM equation.

GCF(2208,2228) = 4
LCM(2208,2228) = ( 2208 × 2228) / 4
LCM(2208,2228) = 4919424 / 4
LCM(2208,2228) = 1229856

Least Common Multiple (LCM) of 2208 and 2228 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2208 and 2228. First we will calculate the prime factors of 2208 and 2228.

Prime Factorization of 2208

Prime Factorization of 2228

Now multiplying the highest exponent prime factors to calculate the LCM of 2208 and 2228.

LCM(2208,2228) = 2⁵ × 3¹ × 23¹ × 557¹
LCM(2208,2228) = 1229856