What is the Least Common Multiple of 5184 and 5200?

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 5184 and 5200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5184 and 5200, than apply into the LCM equation.

GCF(5184,5200) = 16
LCM(5184,5200) = ( 5184 × 5200) / 16
LCM(5184,5200) = 26956800 / 16
LCM(5184,5200) = 1684800

Least Common Multiple (LCM) of 5184 and 5200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5184 and 5200. First we will calculate the prime factors of 5184 and 5200.

Prime Factorization of 5184

Prime Factorization of 5200

Now multiplying the highest exponent prime factors to calculate the LCM of 5184 and 5200.

LCM(5184,5200) = 2⁶ × 3⁴ × 5² × 13¹
LCM(5184,5200) = 1684800