What is the Least Common Multiple of 85744 and 85760?

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 85744 and 85760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85744 and 85760, than apply into the LCM equation.

GCF(85744,85760) = 16
LCM(85744,85760) = ( 85744 × 85760) / 16
LCM(85744,85760) = 7353405440 / 16
LCM(85744,85760) = 459587840

Least Common Multiple (LCM) of 85744 and 85760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85744 and 85760. First we will calculate the prime factors of 85744 and 85760.

Prime Factorization of 85744

Prime Factorization of 85760

Now multiplying the highest exponent prime factors to calculate the LCM of 85744 and 85760.

LCM(85744,85760) = 2⁸ × 23¹ × 233¹ × 5¹ × 67¹
LCM(85744,85760) = 459587840