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What is the Least Common Multiple of 31089 and 31100?

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 (LCM) of 31089 and 31100 is 966867900.

LCM(31089,31100) = 966867900

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Least Common Multiple of 31089 and 31100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31089 and 31100, than apply into the LCM equation.

GCF(31089,31100) = 1
LCM(31089,31100) = ( 31089 × 31100) / 1
LCM(31089,31100) = 966867900 / 1
LCM(31089,31100) = 966867900

Least Common Multiple (LCM) of 31089 and 31100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31089 and 31100. First we will calculate the prime factors of 31089 and 31100.

Prime Factorization of 31089

Prime factors of 31089 are 3, 43, 241. Prime factorization of 31089 in exponential form is:

31089 = 31 × 431 × 2411

Prime Factorization of 31100

Prime factors of 31100 are 2, 5, 311. Prime factorization of 31100 in exponential form is:

31100 = 22 × 52 × 3111

Now multiplying the highest exponent prime factors to calculate the LCM of 31089 and 31100.

LCM(31089,31100) = 31 × 431 × 2411 × 22 × 52 × 3111
LCM(31089,31100) = 966867900