What is the Least Common Multiple of 34575 and 34584?

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 34575 and 34584 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34575 and 34584, than apply into the LCM equation.

GCF(34575,34584) = 3
LCM(34575,34584) = ( 34575 × 34584) / 3
LCM(34575,34584) = 1195741800 / 3
LCM(34575,34584) = 398580600

Least Common Multiple (LCM) of 34575 and 34584 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34575 and 34584. First we will calculate the prime factors of 34575 and 34584.

Prime Factorization of 34575

Prime Factorization of 34584

Now multiplying the highest exponent prime factors to calculate the LCM of 34575 and 34584.

LCM(34575,34584) = 3¹ × 5² × 461¹ × 2³ × 11¹ × 131¹
LCM(34575,34584) = 398580600