What is the Least Common Multiple of 6780 and 6789?

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 6780 and 6789 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6780 and 6789, than apply into the LCM equation.

GCF(6780,6789) = 3
LCM(6780,6789) = ( 6780 × 6789) / 3
LCM(6780,6789) = 46029420 / 3
LCM(6780,6789) = 15343140

Least Common Multiple (LCM) of 6780 and 6789 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6780 and 6789. First we will calculate the prime factors of 6780 and 6789.

Prime Factorization of 6780

Prime Factorization of 6789

Now multiplying the highest exponent prime factors to calculate the LCM of 6780 and 6789.

LCM(6780,6789) = 2² × 3¹ × 5¹ × 113¹ × 31¹ × 73¹
LCM(6780,6789) = 15343140