What is the Least Common Multiple of 19306 and 19314?

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 19306 and 19314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19306 and 19314, than apply into the LCM equation.

GCF(19306,19314) = 2
LCM(19306,19314) = ( 19306 × 19314) / 2
LCM(19306,19314) = 372876084 / 2
LCM(19306,19314) = 186438042

Least Common Multiple (LCM) of 19306 and 19314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19306 and 19314. First we will calculate the prime factors of 19306 and 19314.

Prime Factorization of 19306

Prime Factorization of 19314

Now multiplying the highest exponent prime factors to calculate the LCM of 19306 and 19314.

LCM(19306,19314) = 2¹ × 7² × 197¹ × 3² × 29¹ × 37¹
LCM(19306,19314) = 186438042