What is the Least Common Multiple of 9900 and 9920?

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 9920 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 9920, than apply into the LCM equation.

GCF(9900,9920) = 20
LCM(9900,9920) = ( 9900 × 9920) / 20
LCM(9900,9920) = 98208000 / 20
LCM(9900,9920) = 4910400

Least Common Multiple (LCM) of 9900 and 9920 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9900 and 9920. First we will calculate the prime factors of 9900 and 9920.

Prime Factorization of 9900

Prime Factorization of 9920

Now multiplying the highest exponent prime factors to calculate the LCM of 9900 and 9920.

LCM(9900,9920) = 2⁶ × 3² × 5² × 11¹ × 31¹
LCM(9900,9920) = 4910400