What is the Least Common Multiple of 85806 and 85824?

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 85806 and 85824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85806 and 85824, than apply into the LCM equation.

GCF(85806,85824) = 18
LCM(85806,85824) = ( 85806 × 85824) / 18
LCM(85806,85824) = 7364214144 / 18
LCM(85806,85824) = 409123008

Least Common Multiple (LCM) of 85806 and 85824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85806 and 85824. First we will calculate the prime factors of 85806 and 85824.

Prime Factorization of 85806

Prime Factorization of 85824

Now multiplying the highest exponent prime factors to calculate the LCM of 85806 and 85824.

LCM(85806,85824) = 2⁶ × 3³ × 7¹ × 227¹ × 149¹
LCM(85806,85824) = 409123008