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What is the Least Common Multiple of 31096 and 31109?

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 31096 and 31109 is 74412728.

LCM(31096,31109) = 74412728

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Least Common Multiple of 31096 and 31109 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31096 and 31109, than apply into the LCM equation.

GCF(31096,31109) = 13
LCM(31096,31109) = ( 31096 × 31109) / 13
LCM(31096,31109) = 967365464 / 13
LCM(31096,31109) = 74412728

Least Common Multiple (LCM) of 31096 and 31109 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31096 and 31109. First we will calculate the prime factors of 31096 and 31109.

Prime Factorization of 31096

Prime factors of 31096 are 2, 13, 23. Prime factorization of 31096 in exponential form is:

31096 = 23 × 132 × 231

Prime Factorization of 31109

Prime factors of 31109 are 13, 2393. Prime factorization of 31109 in exponential form is:

31109 = 131 × 23931

Now multiplying the highest exponent prime factors to calculate the LCM of 31096 and 31109.

LCM(31096,31109) = 23 × 132 × 231 × 23931
LCM(31096,31109) = 74412728