What is the Least Common Multiple of 7854 and 7872?

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 7854 and 7872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7854 and 7872, than apply into the LCM equation.

GCF(7854,7872) = 6
LCM(7854,7872) = ( 7854 × 7872) / 6
LCM(7854,7872) = 61826688 / 6
LCM(7854,7872) = 10304448

Least Common Multiple (LCM) of 7854 and 7872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7854 and 7872. First we will calculate the prime factors of 7854 and 7872.

Prime Factorization of 7854

Prime Factorization of 7872

Now multiplying the highest exponent prime factors to calculate the LCM of 7854 and 7872.

LCM(7854,7872) = 2⁶ × 3¹ × 7¹ × 11¹ × 17¹ × 41¹
LCM(7854,7872) = 10304448