What is the Least Common Multiple of 2560 and 2569?

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 2560 and 2569 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2560 and 2569, than apply into the LCM equation.

GCF(2560,2569) = 1
LCM(2560,2569) = ( 2560 × 2569) / 1
LCM(2560,2569) = 6576640 / 1
LCM(2560,2569) = 6576640

Least Common Multiple (LCM) of 2560 and 2569 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2560 and 2569. First we will calculate the prime factors of 2560 and 2569.

Prime Factorization of 2560

Prime Factorization of 2569

Now multiplying the highest exponent prime factors to calculate the LCM of 2560 and 2569.

LCM(2560,2569) = 2⁹ × 5¹ × 7¹ × 367¹
LCM(2560,2569) = 6576640