What is the Least Common Multiple of 1296 and 1309?

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 1296 and 1309 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1296 and 1309, than apply into the LCM equation.

GCF(1296,1309) = 1
LCM(1296,1309) = ( 1296 × 1309) / 1
LCM(1296,1309) = 1696464 / 1
LCM(1296,1309) = 1696464

Least Common Multiple (LCM) of 1296 and 1309 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1296 and 1309. First we will calculate the prime factors of 1296 and 1309.

Prime Factorization of 1296

Prime Factorization of 1309

Now multiplying the highest exponent prime factors to calculate the LCM of 1296 and 1309.

LCM(1296,1309) = 2⁴ × 3⁴ × 7¹ × 11¹ × 17¹
LCM(1296,1309) = 1696464