What is the Least Common Multiple of 82320 and 82338?

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 82338 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 82338, than apply into the LCM equation.

GCF(82320,82338) = 6
LCM(82320,82338) = ( 82320 × 82338) / 6
LCM(82320,82338) = 6778064160 / 6
LCM(82320,82338) = 1129677360

Least Common Multiple (LCM) of 82320 and 82338 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82320 and 82338. First we will calculate the prime factors of 82320 and 82338.

Prime Factorization of 82320

Prime Factorization of 82338

Now multiplying the highest exponent prime factors to calculate the LCM of 82320 and 82338.

LCM(82320,82338) = 2⁴ × 3¹ × 5¹ × 7³ × 13723¹
LCM(82320,82338) = 1129677360