What is the Least Common Multiple of 330 and 345?

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 330 and 345 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 330 and 345, than apply into the LCM equation.

GCF(330,345) = 15
LCM(330,345) = ( 330 × 345) / 15
LCM(330,345) = 113850 / 15
LCM(330,345) = 7590

Least Common Multiple (LCM) of 330 and 345 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 330 and 345. First we will calculate the prime factors of 330 and 345.

Prime Factorization of 330

Prime Factorization of 345

Now multiplying the highest exponent prime factors to calculate the LCM of 330 and 345.

LCM(330,345) = 2¹ × 3¹ × 5¹ × 11¹ × 23¹
LCM(330,345) = 7590