What is the Least Common Multiple of 23760 and 23776?

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 23760 and 23776 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23760 and 23776, than apply into the LCM equation.

GCF(23760,23776) = 16
LCM(23760,23776) = ( 23760 × 23776) / 16
LCM(23760,23776) = 564917760 / 16
LCM(23760,23776) = 35307360

Least Common Multiple (LCM) of 23760 and 23776 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23760 and 23776. First we will calculate the prime factors of 23760 and 23776.

Prime Factorization of 23760

Prime Factorization of 23776

Now multiplying the highest exponent prime factors to calculate the LCM of 23760 and 23776.

LCM(23760,23776) = 2⁵ × 3³ × 5¹ × 11¹ × 743¹
LCM(23760,23776) = 35307360