What is the Least Common Multiple of 6993 and 7000?

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 6993 and 7000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6993 and 7000, than apply into the LCM equation.

GCF(6993,7000) = 7
LCM(6993,7000) = ( 6993 × 7000) / 7
LCM(6993,7000) = 48951000 / 7
LCM(6993,7000) = 6993000

Least Common Multiple (LCM) of 6993 and 7000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6993 and 7000. First we will calculate the prime factors of 6993 and 7000.

Prime Factorization of 6993

Prime Factorization of 7000

Now multiplying the highest exponent prime factors to calculate the LCM of 6993 and 7000.

LCM(6993,7000) = 3³ × 7¹ × 37¹ × 2³ × 5³
LCM(6993,7000) = 6993000