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What is the Least Common Multiple of 31198 and 31212?

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 31212 is 486875988.

LCM(31198,31212) = 486875988

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Least Common Multiple of 31198 and 31212 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 31212, than apply into the LCM equation.

GCF(31198,31212) = 2
LCM(31198,31212) = ( 31198 × 31212) / 2
LCM(31198,31212) = 973751976 / 2
LCM(31198,31212) = 486875988

Least Common Multiple (LCM) of 31198 and 31212 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31198 and 31212. First we will calculate the prime factors of 31198 and 31212.

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 31212

Prime factors of 31212 are 2, 3, 17. Prime factorization of 31212 in exponential form is:

31212 = 22 × 33 × 172

Now multiplying the highest exponent prime factors to calculate the LCM of 31198 and 31212.

LCM(31198,31212) = 22 × 191 × 8211 × 33 × 172
LCM(31198,31212) = 486875988