What is the Least Common Multiple of 31682 and 31696?

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 31682 and 31696 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31682 and 31696, than apply into the LCM equation.

GCF(31682,31696) = 14
LCM(31682,31696) = ( 31682 × 31696) / 14
LCM(31682,31696) = 1004192672 / 14
LCM(31682,31696) = 71728048

Least Common Multiple (LCM) of 31682 and 31696 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31682 and 31696. First we will calculate the prime factors of 31682 and 31696.

Prime Factorization of 31682

Prime Factorization of 31696

Now multiplying the highest exponent prime factors to calculate the LCM of 31682 and 31696.

LCM(31682,31696) = 2⁴ × 7¹ × 31¹ × 73¹ × 283¹
LCM(31682,31696) = 71728048