What is the Least Common Multiple of 1100 and 1108?

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 1100 and 1108 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1100 and 1108, than apply into the LCM equation.

GCF(1100,1108) = 4
LCM(1100,1108) = ( 1100 × 1108) / 4
LCM(1100,1108) = 1218800 / 4
LCM(1100,1108) = 304700

Least Common Multiple (LCM) of 1100 and 1108 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1100 and 1108. First we will calculate the prime factors of 1100 and 1108.

Prime Factorization of 1100

Prime Factorization of 1108

Now multiplying the highest exponent prime factors to calculate the LCM of 1100 and 1108.

LCM(1100,1108) = 2² × 5² × 11¹ × 277¹
LCM(1100,1108) = 304700