What is the Least Common Multiple of 30192 and 30209?

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 30192 and 30209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30192 and 30209, than apply into the LCM equation.

GCF(30192,30209) = 17
LCM(30192,30209) = ( 30192 × 30209) / 17
LCM(30192,30209) = 912070128 / 17
LCM(30192,30209) = 53651184

Least Common Multiple (LCM) of 30192 and 30209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30192 and 30209. First we will calculate the prime factors of 30192 and 30209.

Prime Factorization of 30192

Prime Factorization of 30209

Now multiplying the highest exponent prime factors to calculate the LCM of 30192 and 30209.

LCM(30192,30209) = 2⁴ × 3¹ × 17¹ × 37¹ × 1777¹
LCM(30192,30209) = 53651184