What is the Least Common Multiple of 9750 and 9760?

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 9750 and 9760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9750 and 9760, than apply into the LCM equation.

GCF(9750,9760) = 10
LCM(9750,9760) = ( 9750 × 9760) / 10
LCM(9750,9760) = 95160000 / 10
LCM(9750,9760) = 9516000

Least Common Multiple (LCM) of 9750 and 9760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9750 and 9760. First we will calculate the prime factors of 9750 and 9760.

Prime Factorization of 9750

Prime Factorization of 9760

Now multiplying the highest exponent prime factors to calculate the LCM of 9750 and 9760.

LCM(9750,9760) = 2⁵ × 3¹ × 5³ × 13¹ × 61¹
LCM(9750,9760) = 9516000