What is the Least Common Multiple of 30336 and 30342?

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 30336 and 30342 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30336 and 30342, than apply into the LCM equation.

GCF(30336,30342) = 6
LCM(30336,30342) = ( 30336 × 30342) / 6
LCM(30336,30342) = 920454912 / 6
LCM(30336,30342) = 153409152

Least Common Multiple (LCM) of 30336 and 30342 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30336 and 30342. First we will calculate the prime factors of 30336 and 30342.

Prime Factorization of 30336

Prime Factorization of 30342

Now multiplying the highest exponent prime factors to calculate the LCM of 30336 and 30342.

LCM(30336,30342) = 2⁷ × 3¹ × 79¹ × 13¹ × 389¹
LCM(30336,30342) = 153409152