What is the Least Common Multiple of 23744 and 23760?

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 23744 and 23760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 23744 and 23760, than apply into the LCM equation.

GCF(23744,23760) = 16
LCM(23744,23760) = ( 23744 × 23760) / 16
LCM(23744,23760) = 564157440 / 16
LCM(23744,23760) = 35259840

Least Common Multiple (LCM) of 23744 and 23760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 23744 and 23760. First we will calculate the prime factors of 23744 and 23760.

Prime Factorization of 23744

Prime Factorization of 23760

Now multiplying the highest exponent prime factors to calculate the LCM of 23744 and 23760.

LCM(23744,23760) = 2⁶ × 7¹ × 53¹ × 3³ × 5¹ × 11¹
LCM(23744,23760) = 35259840