What is the Least Common Multiple of 31822 and 31840?

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 31822 and 31840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31822 and 31840, than apply into the LCM equation.

GCF(31822,31840) = 2
LCM(31822,31840) = ( 31822 × 31840) / 2
LCM(31822,31840) = 1013212480 / 2
LCM(31822,31840) = 506606240

Least Common Multiple (LCM) of 31822 and 31840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31822 and 31840. First we will calculate the prime factors of 31822 and 31840.

Prime Factorization of 31822

Prime Factorization of 31840

Now multiplying the highest exponent prime factors to calculate the LCM of 31822 and 31840.

LCM(31822,31840) = 2⁵ × 7¹ × 2273¹ × 5¹ × 199¹
LCM(31822,31840) = 506606240