What is the Least Common Multiple of 51744 and 51760?

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 51744 and 51760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51744 and 51760, than apply into the LCM equation.

GCF(51744,51760) = 16
LCM(51744,51760) = ( 51744 × 51760) / 16
LCM(51744,51760) = 2678269440 / 16
LCM(51744,51760) = 167391840

Least Common Multiple (LCM) of 51744 and 51760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51744 and 51760. First we will calculate the prime factors of 51744 and 51760.

Prime Factorization of 51744

Prime Factorization of 51760

Now multiplying the highest exponent prime factors to calculate the LCM of 51744 and 51760.

LCM(51744,51760) = 2⁵ × 3¹ × 7² × 11¹ × 5¹ × 647¹
LCM(51744,51760) = 167391840