What is the Least Common Multiple of 9876 and 9888?

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 9876 and 9888 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9876 and 9888, than apply into the LCM equation.

GCF(9876,9888) = 12
LCM(9876,9888) = ( 9876 × 9888) / 12
LCM(9876,9888) = 97653888 / 12
LCM(9876,9888) = 8137824

Least Common Multiple (LCM) of 9876 and 9888 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9876 and 9888. First we will calculate the prime factors of 9876 and 9888.

Prime Factorization of 9876

Prime Factorization of 9888

Now multiplying the highest exponent prime factors to calculate the LCM of 9876 and 9888.

LCM(9876,9888) = 2⁵ × 3¹ × 823¹ × 103¹
LCM(9876,9888) = 8137824