What is the Least Common Multiple of 7185 and 7200?

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 7185 and 7200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7185 and 7200, than apply into the LCM equation.

GCF(7185,7200) = 15
LCM(7185,7200) = ( 7185 × 7200) / 15
LCM(7185,7200) = 51732000 / 15
LCM(7185,7200) = 3448800

Least Common Multiple (LCM) of 7185 and 7200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7185 and 7200. First we will calculate the prime factors of 7185 and 7200.

Prime Factorization of 7185

Prime Factorization of 7200

Now multiplying the highest exponent prime factors to calculate the LCM of 7185 and 7200.

LCM(7185,7200) = 3² × 5² × 479¹ × 2⁵
LCM(7185,7200) = 3448800