What is the Least Common Multiple of 810 and 828?

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 828 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 828, than apply into the LCM equation.

GCF(810,828) = 18
LCM(810,828) = ( 810 × 828) / 18
LCM(810,828) = 670680 / 18
LCM(810,828) = 37260

Least Common Multiple (LCM) of 810 and 828 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 810 and 828. First we will calculate the prime factors of 810 and 828.

Prime Factorization of 810

Prime Factorization of 828

Now multiplying the highest exponent prime factors to calculate the LCM of 810 and 828.

LCM(810,828) = 2² × 3⁴ × 5¹ × 23¹
LCM(810,828) = 37260