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What is the Least Common Multiple of 12 and 31?

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 12 and 31 is 372.

LCM(12,31) = 372

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Least Common Multiple of 12 and 31 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 31, than apply into the LCM equation.

GCF(12,31) = 1
LCM(12,31) = ( 12 × 31) / 1
LCM(12,31) = 372 / 1
LCM(12,31) = 372

Least Common Multiple (LCM) of 12 and 31 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 31. First we will calculate the prime factors of 12 and 31.

Prime Factorization of 12

Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:

12 = 22 × 31

Prime Factorization of 31

Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:

31 = 311

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 31.

LCM(12,31) = 22 × 31 × 311
LCM(12,31) = 372

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