What is the Least Common Multiple of 82297 and 82314?

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 82297 and 82314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82297 and 82314, than apply into the LCM equation.

GCF(82297,82314) = 17
LCM(82297,82314) = ( 82297 × 82314) / 17
LCM(82297,82314) = 6774195258 / 17
LCM(82297,82314) = 398482074

Least Common Multiple (LCM) of 82297 and 82314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82297 and 82314. First we will calculate the prime factors of 82297 and 82314.

Prime Factorization of 82297

Prime Factorization of 82314

Now multiplying the highest exponent prime factors to calculate the LCM of 82297 and 82314.

LCM(82297,82314) = 17¹ × 47¹ × 103¹ × 2¹ × 3² × 269¹
LCM(82297,82314) = 398482074