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What is the Least Common Multiple of 31198 and 31209?

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 31198 and 31209 is 973658382.

LCM(31198,31209) = 973658382

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Least Common Multiple of 31198 and 31209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31198 and 31209, than apply into the LCM equation.

GCF(31198,31209) = 1
LCM(31198,31209) = ( 31198 × 31209) / 1
LCM(31198,31209) = 973658382 / 1
LCM(31198,31209) = 973658382

Least Common Multiple (LCM) of 31198 and 31209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31198 and 31209. First we will calculate the prime factors of 31198 and 31209.

Prime Factorization of 31198

Prime factors of 31198 are 2, 19, 821. Prime factorization of 31198 in exponential form is:

31198 = 21 × 191 × 8211

Prime Factorization of 31209

Prime factors of 31209 are 3, 101, 103. Prime factorization of 31209 in exponential form is:

31209 = 31 × 1011 × 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 31198 and 31209.

LCM(31198,31209) = 21 × 191 × 8211 × 31 × 1011 × 1031
LCM(31198,31209) = 973658382