What is the Least Common Multiple of 9900 and 9915?

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 9900 and 9915 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9900 and 9915, than apply into the LCM equation.

GCF(9900,9915) = 15
LCM(9900,9915) = ( 9900 × 9915) / 15
LCM(9900,9915) = 98158500 / 15
LCM(9900,9915) = 6543900

Least Common Multiple (LCM) of 9900 and 9915 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9900 and 9915. First we will calculate the prime factors of 9900 and 9915.

Prime Factorization of 9900

Prime Factorization of 9915

Now multiplying the highest exponent prime factors to calculate the LCM of 9900 and 9915.

LCM(9900,9915) = 2² × 3² × 5² × 11¹ × 661¹
LCM(9900,9915) = 6543900