What is the Least Common Multiple of 9975 and 9984?

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 9975 and 9984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9975 and 9984, than apply into the LCM equation.

GCF(9975,9984) = 3
LCM(9975,9984) = ( 9975 × 9984) / 3
LCM(9975,9984) = 99590400 / 3
LCM(9975,9984) = 33196800

Least Common Multiple (LCM) of 9975 and 9984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9975 and 9984. First we will calculate the prime factors of 9975 and 9984.

Prime Factorization of 9975

Prime Factorization of 9984

Now multiplying the highest exponent prime factors to calculate the LCM of 9975 and 9984.

LCM(9975,9984) = 3¹ × 5² × 7¹ × 19¹ × 2⁸ × 13¹
LCM(9975,9984) = 33196800