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What is the Least Common Multiple of 31119 and 31130?

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 31119 and 31130 is 88066770.

LCM(31119,31130) = 88066770

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Least Common Multiple of 31119 and 31130 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31119 and 31130, than apply into the LCM equation.

GCF(31119,31130) = 11
LCM(31119,31130) = ( 31119 × 31130) / 11
LCM(31119,31130) = 968734470 / 11
LCM(31119,31130) = 88066770

Least Common Multiple (LCM) of 31119 and 31130 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31119 and 31130. First we will calculate the prime factors of 31119 and 31130.

Prime Factorization of 31119

Prime factors of 31119 are 3, 11, 23, 41. Prime factorization of 31119 in exponential form is:

31119 = 31 × 111 × 231 × 411

Prime Factorization of 31130

Prime factors of 31130 are 2, 5, 11, 283. Prime factorization of 31130 in exponential form is:

31130 = 21 × 51 × 111 × 2831

Now multiplying the highest exponent prime factors to calculate the LCM of 31119 and 31130.

LCM(31119,31130) = 31 × 111 × 231 × 411 × 21 × 51 × 2831
LCM(31119,31130) = 88066770