What is the Least Common Multiple of 17184 and 17200?

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 17184 and 17200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17184 and 17200, than apply into the LCM equation.

GCF(17184,17200) = 16
LCM(17184,17200) = ( 17184 × 17200) / 16
LCM(17184,17200) = 295564800 / 16
LCM(17184,17200) = 18472800

Least Common Multiple (LCM) of 17184 and 17200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17184 and 17200. First we will calculate the prime factors of 17184 and 17200.

Prime Factorization of 17184

Prime Factorization of 17200

Now multiplying the highest exponent prime factors to calculate the LCM of 17184 and 17200.

LCM(17184,17200) = 2⁵ × 3¹ × 179¹ × 5² × 43¹
LCM(17184,17200) = 18472800