What is the Least Common Multiple of 34560 and 34575?

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 34560 and 34575 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34560 and 34575, than apply into the LCM equation.

GCF(34560,34575) = 15
LCM(34560,34575) = ( 34560 × 34575) / 15
LCM(34560,34575) = 1194912000 / 15
LCM(34560,34575) = 79660800

Least Common Multiple (LCM) of 34560 and 34575 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34560 and 34575. First we will calculate the prime factors of 34560 and 34575.

Prime Factorization of 34560

Prime Factorization of 34575

Now multiplying the highest exponent prime factors to calculate the LCM of 34560 and 34575.

LCM(34560,34575) = 2⁸ × 3³ × 5² × 461¹
LCM(34560,34575) = 79660800