What is the Least Common Multiple of 82320 and 82329?

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 82320 and 82329 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82320 and 82329, than apply into the LCM equation.

GCF(82320,82329) = 3
LCM(82320,82329) = ( 82320 × 82329) / 3
LCM(82320,82329) = 6777323280 / 3
LCM(82320,82329) = 2259107760

Least Common Multiple (LCM) of 82320 and 82329 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82320 and 82329. First we will calculate the prime factors of 82320 and 82329.

Prime Factorization of 82320

Prime Factorization of 82329

Now multiplying the highest exponent prime factors to calculate the LCM of 82320 and 82329.

LCM(82320,82329) = 2⁴ × 3¹ × 5¹ × 7³ × 13¹ × 2111¹
LCM(82320,82329) = 2259107760