What is the Least Common Multiple of 12704 and 12714?

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 12704 and 12714 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12704 and 12714, than apply into the LCM equation.

GCF(12704,12714) = 2
LCM(12704,12714) = ( 12704 × 12714) / 2
LCM(12704,12714) = 161518656 / 2
LCM(12704,12714) = 80759328

Least Common Multiple (LCM) of 12704 and 12714 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12704 and 12714. First we will calculate the prime factors of 12704 and 12714.

Prime Factorization of 12704

Prime Factorization of 12714

Now multiplying the highest exponent prime factors to calculate the LCM of 12704 and 12714.

LCM(12704,12714) = 2⁵ × 397¹ × 3¹ × 13¹ × 163¹
LCM(12704,12714) = 80759328