What is the Least Common Multiple of 8302 and 8314?

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 8302 and 8314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8302 and 8314, than apply into the LCM equation.

GCF(8302,8314) = 2
LCM(8302,8314) = ( 8302 × 8314) / 2
LCM(8302,8314) = 69022828 / 2
LCM(8302,8314) = 34511414

Least Common Multiple (LCM) of 8302 and 8314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8302 and 8314. First we will calculate the prime factors of 8302 and 8314.

Prime Factorization of 8302

Prime Factorization of 8314

Now multiplying the highest exponent prime factors to calculate the LCM of 8302 and 8314.

LCM(8302,8314) = 2¹ × 7¹ × 593¹ × 4157¹
LCM(8302,8314) = 34511414