What is the Least Common Multiple of 15306 and 15314?

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 15306 and 15314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15306 and 15314, than apply into the LCM equation.

GCF(15306,15314) = 2
LCM(15306,15314) = ( 15306 × 15314) / 2
LCM(15306,15314) = 234396084 / 2
LCM(15306,15314) = 117198042

Least Common Multiple (LCM) of 15306 and 15314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15306 and 15314. First we will calculate the prime factors of 15306 and 15314.

Prime Factorization of 15306

Prime Factorization of 15314

Now multiplying the highest exponent prime factors to calculate the LCM of 15306 and 15314.

LCM(15306,15314) = 2¹ × 3¹ × 2551¹ × 13¹ × 19¹ × 31¹
LCM(15306,15314) = 117198042