What is the Least Common Multiple of 810 and 825?

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 810 and 825 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 810 and 825, than apply into the LCM equation.

GCF(810,825) = 15
LCM(810,825) = ( 810 × 825) / 15
LCM(810,825) = 668250 / 15
LCM(810,825) = 44550

Least Common Multiple (LCM) of 810 and 825 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 810 and 825. First we will calculate the prime factors of 810 and 825.

Prime Factorization of 810

Prime Factorization of 825

Now multiplying the highest exponent prime factors to calculate the LCM of 810 and 825.

LCM(810,825) = 2¹ × 3⁴ × 5² × 11¹
LCM(810,825) = 44550