What is the Least Common Multiple of 9975 and 9980?

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 9980 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 9980, than apply into the LCM equation.

GCF(9975,9980) = 5
LCM(9975,9980) = ( 9975 × 9980) / 5
LCM(9975,9980) = 99550500 / 5
LCM(9975,9980) = 19910100

Least Common Multiple (LCM) of 9975 and 9980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9975 and 9980. First we will calculate the prime factors of 9975 and 9980.

Prime Factorization of 9975

Prime Factorization of 9980

Now multiplying the highest exponent prime factors to calculate the LCM of 9975 and 9980.

LCM(9975,9980) = 3¹ × 5² × 7¹ × 19¹ × 2² × 499¹
LCM(9975,9980) = 19910100