What is the Least Common Multiple of 9968 and 9975?

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 9968 and 9975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9968 and 9975, than apply into the LCM equation.

GCF(9968,9975) = 7
LCM(9968,9975) = ( 9968 × 9975) / 7
LCM(9968,9975) = 99430800 / 7
LCM(9968,9975) = 14204400

Least Common Multiple (LCM) of 9968 and 9975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9968 and 9975. First we will calculate the prime factors of 9968 and 9975.

Prime Factorization of 9968

Prime Factorization of 9975

Now multiplying the highest exponent prime factors to calculate the LCM of 9968 and 9975.

LCM(9968,9975) = 2⁴ × 7¹ × 89¹ × 3¹ × 5² × 19¹
LCM(9968,9975) = 14204400