What is the Least Common Multiple of 9500 and 9504?

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 9500 and 9504 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9500 and 9504, than apply into the LCM equation.

GCF(9500,9504) = 4
LCM(9500,9504) = ( 9500 × 9504) / 4
LCM(9500,9504) = 90288000 / 4
LCM(9500,9504) = 22572000

Least Common Multiple (LCM) of 9500 and 9504 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9500 and 9504. First we will calculate the prime factors of 9500 and 9504.

Prime Factorization of 9500

Prime Factorization of 9504

Now multiplying the highest exponent prime factors to calculate the LCM of 9500 and 9504.

LCM(9500,9504) = 2⁵ × 5³ × 19¹ × 3³ × 11¹
LCM(9500,9504) = 22572000