What is the Least Common Multiple of 85734 and 85749?

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 85734 and 85749 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85734 and 85749, than apply into the LCM equation.

GCF(85734,85749) = 3
LCM(85734,85749) = ( 85734 × 85749) / 3
LCM(85734,85749) = 7351604766 / 3
LCM(85734,85749) = 2450534922

Least Common Multiple (LCM) of 85734 and 85749 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85734 and 85749. First we will calculate the prime factors of 85734 and 85749.

Prime Factorization of 85734

Prime Factorization of 85749

Now multiplying the highest exponent prime factors to calculate the LCM of 85734 and 85749.

LCM(85734,85749) = 2¹ × 3² × 11¹ × 433¹ × 101¹ × 283¹
LCM(85734,85749) = 2450534922