What is the Least Common Multiple of 6789 and 6800?

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 6789 and 6800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6789 and 6800, than apply into the LCM equation.

GCF(6789,6800) = 1
LCM(6789,6800) = ( 6789 × 6800) / 1
LCM(6789,6800) = 46165200 / 1
LCM(6789,6800) = 46165200

Least Common Multiple (LCM) of 6789 and 6800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6789 and 6800. First we will calculate the prime factors of 6789 and 6800.

Prime Factorization of 6789

Prime Factorization of 6800

Now multiplying the highest exponent prime factors to calculate the LCM of 6789 and 6800.

LCM(6789,6800) = 3¹ × 31¹ × 73¹ × 2⁴ × 5² × 17¹
LCM(6789,6800) = 46165200