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What is the Least Common Multiple of 31000 and 31015?

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 31000 and 31015 is 192293000.

LCM(31000,31015) = 192293000

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Least Common Multiple of 31000 and 31015 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31000 and 31015, than apply into the LCM equation.

GCF(31000,31015) = 5
LCM(31000,31015) = ( 31000 × 31015) / 5
LCM(31000,31015) = 961465000 / 5
LCM(31000,31015) = 192293000

Least Common Multiple (LCM) of 31000 and 31015 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31000 and 31015. First we will calculate the prime factors of 31000 and 31015.

Prime Factorization of 31000

Prime factors of 31000 are 2, 5, 31. Prime factorization of 31000 in exponential form is:

31000 = 23 × 53 × 311

Prime Factorization of 31015

Prime factors of 31015 are 5, 6203. Prime factorization of 31015 in exponential form is:

31015 = 51 × 62031

Now multiplying the highest exponent prime factors to calculate the LCM of 31000 and 31015.

LCM(31000,31015) = 23 × 53 × 311 × 62031
LCM(31000,31015) = 192293000