What is the Least Common Multiple of 81744 and 81760?

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 81744 and 81760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 81744 and 81760, than apply into the LCM equation.

GCF(81744,81760) = 16
LCM(81744,81760) = ( 81744 × 81760) / 16
LCM(81744,81760) = 6683389440 / 16
LCM(81744,81760) = 417711840

Least Common Multiple (LCM) of 81744 and 81760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 81744 and 81760. First we will calculate the prime factors of 81744 and 81760.

Prime Factorization of 81744

Prime Factorization of 81760

Now multiplying the highest exponent prime factors to calculate the LCM of 81744 and 81760.

LCM(81744,81760) = 2⁵ × 3¹ × 13¹ × 131¹ × 5¹ × 7¹ × 73¹
LCM(81744,81760) = 417711840