What is the Least Common Multiple of 30576 and 30590?

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 30590 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 30590, than apply into the LCM equation.

GCF(30576,30590) = 14
LCM(30576,30590) = ( 30576 × 30590) / 14
LCM(30576,30590) = 935319840 / 14
LCM(30576,30590) = 66808560

Least Common Multiple (LCM) of 30576 and 30590 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30576 and 30590. First we will calculate the prime factors of 30576 and 30590.

Prime Factorization of 30576

Prime Factorization of 30590

Now multiplying the highest exponent prime factors to calculate the LCM of 30576 and 30590.

LCM(30576,30590) = 2⁴ × 3¹ × 7² × 13¹ × 5¹ × 19¹ × 23¹
LCM(30576,30590) = 66808560