What is the Least Common Multiple of 1188 and 1200?

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 1188 and 1200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1188 and 1200, than apply into the LCM equation.

GCF(1188,1200) = 12
LCM(1188,1200) = ( 1188 × 1200) / 12
LCM(1188,1200) = 1425600 / 12
LCM(1188,1200) = 118800

Least Common Multiple (LCM) of 1188 and 1200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1188 and 1200. First we will calculate the prime factors of 1188 and 1200.

Prime Factorization of 1188

Prime Factorization of 1200

Now multiplying the highest exponent prime factors to calculate the LCM of 1188 and 1200.

LCM(1188,1200) = 2⁴ × 3³ × 11¹ × 5²
LCM(1188,1200) = 118800