What is the Least Common Multiple of 26000 and 26016?

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 26000 and 26016 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 26000 and 26016, than apply into the LCM equation.

GCF(26000,26016) = 16
LCM(26000,26016) = ( 26000 × 26016) / 16
LCM(26000,26016) = 676416000 / 16
LCM(26000,26016) = 42276000

Least Common Multiple (LCM) of 26000 and 26016 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 26000 and 26016. First we will calculate the prime factors of 26000 and 26016.

Prime Factorization of 26000

Prime Factorization of 26016

Now multiplying the highest exponent prime factors to calculate the LCM of 26000 and 26016.

LCM(26000,26016) = 2⁵ × 5³ × 13¹ × 3¹ × 271¹
LCM(26000,26016) = 42276000