What is the Least Common Multiple of 6816 and 6825?

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 6816 and 6825 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6816 and 6825, than apply into the LCM equation.

GCF(6816,6825) = 3
LCM(6816,6825) = ( 6816 × 6825) / 3
LCM(6816,6825) = 46519200 / 3
LCM(6816,6825) = 15506400

Least Common Multiple (LCM) of 6816 and 6825 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6816 and 6825. First we will calculate the prime factors of 6816 and 6825.

Prime Factorization of 6816

Prime Factorization of 6825

Now multiplying the highest exponent prime factors to calculate the LCM of 6816 and 6825.

LCM(6816,6825) = 2⁵ × 3¹ × 71¹ × 5² × 7¹ × 13¹
LCM(6816,6825) = 15506400