What is the Least Common Multiple of 2200 and 2219?

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 2219 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 2219, than apply into the LCM equation.

GCF(2200,2219) = 1
LCM(2200,2219) = ( 2200 × 2219) / 1
LCM(2200,2219) = 4881800 / 1
LCM(2200,2219) = 4881800

Least Common Multiple (LCM) of 2200 and 2219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2200 and 2219. First we will calculate the prime factors of 2200 and 2219.

Prime Factorization of 2200

Prime Factorization of 2219

Now multiplying the highest exponent prime factors to calculate the LCM of 2200 and 2219.

LCM(2200,2219) = 2³ × 5² × 11¹ × 7¹ × 317¹
LCM(2200,2219) = 4881800