What is the Least Common Multiple of 85824 and 85830?

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 85824 and 85830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 85824 and 85830, than apply into the LCM equation.

GCF(85824,85830) = 6
LCM(85824,85830) = ( 85824 × 85830) / 6
LCM(85824,85830) = 7366273920 / 6
LCM(85824,85830) = 1227712320

Least Common Multiple (LCM) of 85824 and 85830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 85824 and 85830. First we will calculate the prime factors of 85824 and 85830.

Prime Factorization of 85824

Prime Factorization of 85830

Now multiplying the highest exponent prime factors to calculate the LCM of 85824 and 85830.

LCM(85824,85830) = 2⁶ × 3² × 149¹ × 5¹ × 2861¹
LCM(85824,85830) = 1227712320