What is the Least Common Multiple of 82305 and 82320?

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 82305 and 82320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82305 and 82320, than apply into the LCM equation.

GCF(82305,82320) = 15
LCM(82305,82320) = ( 82305 × 82320) / 15
LCM(82305,82320) = 6775347600 / 15
LCM(82305,82320) = 451689840

Least Common Multiple (LCM) of 82305 and 82320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82305 and 82320. First we will calculate the prime factors of 82305 and 82320.

Prime Factorization of 82305

Prime Factorization of 82320

Now multiplying the highest exponent prime factors to calculate the LCM of 82305 and 82320.

LCM(82305,82320) = 3² × 5¹ × 31¹ × 59¹ × 2⁴ × 7³
LCM(82305,82320) = 451689840