What is the Least Common Multiple of 34080 and 34089?

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 34080 and 34089 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34080 and 34089, than apply into the LCM equation.

GCF(34080,34089) = 3
LCM(34080,34089) = ( 34080 × 34089) / 3
LCM(34080,34089) = 1161753120 / 3
LCM(34080,34089) = 387251040

Least Common Multiple (LCM) of 34080 and 34089 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34080 and 34089. First we will calculate the prime factors of 34080 and 34089.

Prime Factorization of 34080

Prime Factorization of 34089

Now multiplying the highest exponent prime factors to calculate the LCM of 34080 and 34089.

LCM(34080,34089) = 2⁵ × 3¹ × 5¹ × 71¹ × 11¹ × 1033¹
LCM(34080,34089) = 387251040