What is the Least Common Multiple of 26500 and 26512?

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 26500 and 26512 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 26500 and 26512, than apply into the LCM equation.

GCF(26500,26512) = 4
LCM(26500,26512) = ( 26500 × 26512) / 4
LCM(26500,26512) = 702568000 / 4
LCM(26500,26512) = 175642000

Least Common Multiple (LCM) of 26500 and 26512 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 26500 and 26512. First we will calculate the prime factors of 26500 and 26512.

Prime Factorization of 26500

Prime Factorization of 26512

Now multiplying the highest exponent prime factors to calculate the LCM of 26500 and 26512.

LCM(26500,26512) = 2⁴ × 5³ × 53¹ × 1657¹
LCM(26500,26512) = 175642000