What is the Least Common Multiple of 31297 and 31314?

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 31297 and 31314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31297 and 31314, than apply into the LCM equation.

GCF(31297,31314) = 17
LCM(31297,31314) = ( 31297 × 31314) / 17
LCM(31297,31314) = 980034258 / 17
LCM(31297,31314) = 57649074

Least Common Multiple (LCM) of 31297 and 31314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31297 and 31314. First we will calculate the prime factors of 31297 and 31314.

Prime Factorization of 31297

Prime Factorization of 31314

Now multiplying the highest exponent prime factors to calculate the LCM of 31297 and 31314.

LCM(31297,31314) = 7¹ × 17¹ × 263¹ × 2¹ × 3¹ × 307¹
LCM(31297,31314) = 57649074