What is the Least Common Multiple of 30576 and 30585?

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 30576 and 30585 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30576 and 30585, than apply into the LCM equation.

GCF(30576,30585) = 3
LCM(30576,30585) = ( 30576 × 30585) / 3
LCM(30576,30585) = 935166960 / 3
LCM(30576,30585) = 311722320

Least Common Multiple (LCM) of 30576 and 30585 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30576 and 30585. First we will calculate the prime factors of 30576 and 30585.

Prime Factorization of 30576

Prime Factorization of 30585

Now multiplying the highest exponent prime factors to calculate the LCM of 30576 and 30585.

LCM(30576,30585) = 2⁴ × 3¹ × 7² × 13¹ × 5¹ × 2039¹
LCM(30576,30585) = 311722320