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What is the Least Common Multiple of 31255 and 31274?

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 31255 and 31274 is 51445730.

LCM(31255,31274) = 51445730

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Least Common Multiple of 31255 and 31274 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31255 and 31274, than apply into the LCM equation.

GCF(31255,31274) = 19
LCM(31255,31274) = ( 31255 × 31274) / 19
LCM(31255,31274) = 977468870 / 19
LCM(31255,31274) = 51445730

Least Common Multiple (LCM) of 31255 and 31274 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31255 and 31274. First we will calculate the prime factors of 31255 and 31274.

Prime Factorization of 31255

Prime factors of 31255 are 5, 7, 19, 47. Prime factorization of 31255 in exponential form is:

31255 = 51 × 71 × 191 × 471

Prime Factorization of 31274

Prime factors of 31274 are 2, 19, 823. Prime factorization of 31274 in exponential form is:

31274 = 21 × 191 × 8231

Now multiplying the highest exponent prime factors to calculate the LCM of 31255 and 31274.

LCM(31255,31274) = 51 × 71 × 191 × 471 × 21 × 8231
LCM(31255,31274) = 51445730