What is the Least Common Multiple of 1100 and 1111?

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 1111 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 1111, than apply into the LCM equation.

GCF(1100,1111) = 11
LCM(1100,1111) = ( 1100 × 1111) / 11
LCM(1100,1111) = 1222100 / 11
LCM(1100,1111) = 111100

Least Common Multiple (LCM) of 1100 and 1111 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1100 and 1111. First we will calculate the prime factors of 1100 and 1111.

Prime Factorization of 1100

Prime Factorization of 1111

Now multiplying the highest exponent prime factors to calculate the LCM of 1100 and 1111.

LCM(1100,1111) = 2² × 5² × 11¹ × 101¹
LCM(1100,1111) = 111100