What is the Least Common Multiple of 31275 and 31284?

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 31275 and 31284 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31275 and 31284, than apply into the LCM equation.

GCF(31275,31284) = 9
LCM(31275,31284) = ( 31275 × 31284) / 9
LCM(31275,31284) = 978407100 / 9
LCM(31275,31284) = 108711900

Least Common Multiple (LCM) of 31275 and 31284 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31275 and 31284. First we will calculate the prime factors of 31275 and 31284.

Prime Factorization of 31275

Prime Factorization of 31284

Now multiplying the highest exponent prime factors to calculate the LCM of 31275 and 31284.

LCM(31275,31284) = 3² × 5² × 139¹ × 2² × 11¹ × 79¹
LCM(31275,31284) = 108711900