What is the Least Common Multiple of 31104 and 31122?

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 31104 and 31122 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31104 and 31122, than apply into the LCM equation.

GCF(31104,31122) = 18
LCM(31104,31122) = ( 31104 × 31122) / 18
LCM(31104,31122) = 968018688 / 18
LCM(31104,31122) = 53778816

Least Common Multiple (LCM) of 31104 and 31122 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31104 and 31122. First we will calculate the prime factors of 31104 and 31122.

Prime Factorization of 31104

Prime Factorization of 31122

Now multiplying the highest exponent prime factors to calculate the LCM of 31104 and 31122.

LCM(31104,31122) = 2⁷ × 3⁵ × 7¹ × 13¹ × 19¹
LCM(31104,31122) = 53778816