What is the Least Common Multiple of 9760 and 9765?

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 9760 and 9765 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9760 and 9765, than apply into the LCM equation.

GCF(9760,9765) = 5
LCM(9760,9765) = ( 9760 × 9765) / 5
LCM(9760,9765) = 95306400 / 5
LCM(9760,9765) = 19061280

Least Common Multiple (LCM) of 9760 and 9765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9760 and 9765. First we will calculate the prime factors of 9760 and 9765.

Prime Factorization of 9760

Prime Factorization of 9765

Now multiplying the highest exponent prime factors to calculate the LCM of 9760 and 9765.

LCM(9760,9765) = 2⁵ × 5¹ × 61¹ × 3² × 7¹ × 31¹
LCM(9760,9765) = 19061280