What is the Least Common Multiple of 6825 and 6840?

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 6825 and 6840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6825 and 6840, than apply into the LCM equation.

GCF(6825,6840) = 15
LCM(6825,6840) = ( 6825 × 6840) / 15
LCM(6825,6840) = 46683000 / 15
LCM(6825,6840) = 3112200

Least Common Multiple (LCM) of 6825 and 6840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6825 and 6840. First we will calculate the prime factors of 6825 and 6840.

Prime Factorization of 6825

Prime Factorization of 6840

Now multiplying the highest exponent prime factors to calculate the LCM of 6825 and 6840.

LCM(6825,6840) = 3² × 5² × 7¹ × 13¹ × 2³ × 19¹
LCM(6825,6840) = 3112200