What is the Least Common Multiple of 39240 and 39249?

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 39240 and 39249 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39240 and 39249, than apply into the LCM equation.

GCF(39240,39249) = 9
LCM(39240,39249) = ( 39240 × 39249) / 9
LCM(39240,39249) = 1540130760 / 9
LCM(39240,39249) = 171125640

Least Common Multiple (LCM) of 39240 and 39249 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39240 and 39249. First we will calculate the prime factors of 39240 and 39249.

Prime Factorization of 39240

Prime Factorization of 39249

Now multiplying the highest exponent prime factors to calculate the LCM of 39240 and 39249.

LCM(39240,39249) = 2³ × 3² × 5¹ × 109¹ × 7² × 89¹
LCM(39240,39249) = 171125640