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What is the Least Common Multiple of 31214 and 31233?

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 31214 and 31233 is 974906862.

LCM(31214,31233) = 974906862

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Least Common Multiple of 31214 and 31233 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31214 and 31233, than apply into the LCM equation.

GCF(31214,31233) = 1
LCM(31214,31233) = ( 31214 × 31233) / 1
LCM(31214,31233) = 974906862 / 1
LCM(31214,31233) = 974906862

Least Common Multiple (LCM) of 31214 and 31233 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31214 and 31233. First we will calculate the prime factors of 31214 and 31233.

Prime Factorization of 31214

Prime factors of 31214 are 2, 15607. Prime factorization of 31214 in exponential form is:

31214 = 21 × 156071

Prime Factorization of 31233

Prime factors of 31233 are 3, 29, 359. Prime factorization of 31233 in exponential form is:

31233 = 31 × 291 × 3591

Now multiplying the highest exponent prime factors to calculate the LCM of 31214 and 31233.

LCM(31214,31233) = 21 × 156071 × 31 × 291 × 3591
LCM(31214,31233) = 974906862