What is the Least Common Multiple of 71314 and 71328?

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 71314 and 71328 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 71314 and 71328, than apply into the LCM equation.

GCF(71314,71328) = 2
LCM(71314,71328) = ( 71314 × 71328) / 2
LCM(71314,71328) = 5086684992 / 2
LCM(71314,71328) = 2543342496

Least Common Multiple (LCM) of 71314 and 71328 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 71314 and 71328. First we will calculate the prime factors of 71314 and 71328.

Prime Factorization of 71314

Prime Factorization of 71328

Now multiplying the highest exponent prime factors to calculate the LCM of 71314 and 71328.

LCM(71314,71328) = 2⁵ × 181¹ × 197¹ × 3¹ × 743¹
LCM(71314,71328) = 2543342496