What is the Least Common Multiple of 1085 and 1100?

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 1085 and 1100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1085 and 1100, than apply into the LCM equation.

GCF(1085,1100) = 5
LCM(1085,1100) = ( 1085 × 1100) / 5
LCM(1085,1100) = 1193500 / 5
LCM(1085,1100) = 238700

Least Common Multiple (LCM) of 1085 and 1100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1085 and 1100. First we will calculate the prime factors of 1085 and 1100.

Prime Factorization of 1085

Prime Factorization of 1100

Now multiplying the highest exponent prime factors to calculate the LCM of 1085 and 1100.

LCM(1085,1100) = 5² × 7¹ × 31¹ × 2² × 11¹
LCM(1085,1100) = 238700