What is the Least Common Multiple of 17296 and 17314?

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 17296 and 17314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17296 and 17314, than apply into the LCM equation.

GCF(17296,17314) = 2
LCM(17296,17314) = ( 17296 × 17314) / 2
LCM(17296,17314) = 299462944 / 2
LCM(17296,17314) = 149731472

Least Common Multiple (LCM) of 17296 and 17314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 17296 and 17314. First we will calculate the prime factors of 17296 and 17314.

Prime Factorization of 17296

Prime Factorization of 17314

Now multiplying the highest exponent prime factors to calculate the LCM of 17296 and 17314.

LCM(17296,17314) = 2⁴ × 23¹ × 47¹ × 11¹ × 787¹
LCM(17296,17314) = 149731472