What is the Least Common Multiple of 21810 and 21825?

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 21810 and 21825 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21810 and 21825, than apply into the LCM equation.

GCF(21810,21825) = 15
LCM(21810,21825) = ( 21810 × 21825) / 15
LCM(21810,21825) = 476003250 / 15
LCM(21810,21825) = 31733550

Least Common Multiple (LCM) of 21810 and 21825 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21810 and 21825. First we will calculate the prime factors of 21810 and 21825.

Prime Factorization of 21810

Prime Factorization of 21825

Now multiplying the highest exponent prime factors to calculate the LCM of 21810 and 21825.

LCM(21810,21825) = 2¹ × 3² × 5² × 727¹ × 97¹
LCM(21810,21825) = 31733550