What is the Least Common Multiple of 15744 and 15760?

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 15744 and 15760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15744 and 15760, than apply into the LCM equation.

GCF(15744,15760) = 16
LCM(15744,15760) = ( 15744 × 15760) / 16
LCM(15744,15760) = 248125440 / 16
LCM(15744,15760) = 15507840

Least Common Multiple (LCM) of 15744 and 15760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15744 and 15760. First we will calculate the prime factors of 15744 and 15760.

Prime Factorization of 15744

Prime Factorization of 15760

Now multiplying the highest exponent prime factors to calculate the LCM of 15744 and 15760.

LCM(15744,15760) = 2⁷ × 3¹ × 41¹ × 5¹ × 197¹
LCM(15744,15760) = 15507840