What is the Least Common Multiple of 21500 and 21520?

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 21500 and 21520 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21500 and 21520, than apply into the LCM equation.

GCF(21500,21520) = 20
LCM(21500,21520) = ( 21500 × 21520) / 20
LCM(21500,21520) = 462680000 / 20
LCM(21500,21520) = 23134000

Least Common Multiple (LCM) of 21500 and 21520 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21500 and 21520. First we will calculate the prime factors of 21500 and 21520.

Prime Factorization of 21500

Prime Factorization of 21520

Now multiplying the highest exponent prime factors to calculate the LCM of 21500 and 21520.

LCM(21500,21520) = 2⁴ × 5³ × 43¹ × 269¹
LCM(21500,21520) = 23134000