What is the Least Common Multiple of 26000 and 26005?

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 26005 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 26005, than apply into the LCM equation.

GCF(26000,26005) = 5
LCM(26000,26005) = ( 26000 × 26005) / 5
LCM(26000,26005) = 676130000 / 5
LCM(26000,26005) = 135226000

Least Common Multiple (LCM) of 26000 and 26005 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 26000 and 26005. First we will calculate the prime factors of 26000 and 26005.

Prime Factorization of 26000

Prime Factorization of 26005

Now multiplying the highest exponent prime factors to calculate the LCM of 26000 and 26005.

LCM(26000,26005) = 2⁴ × 5³ × 13¹ × 7¹ × 743¹
LCM(26000,26005) = 135226000