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What is the Least Common Multiple of 31205 and 31222?

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 31205 and 31222 is 974282510.

LCM(31205,31222) = 974282510

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Least Common Multiple of 31205 and 31222 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31205 and 31222, than apply into the LCM equation.

GCF(31205,31222) = 1
LCM(31205,31222) = ( 31205 × 31222) / 1
LCM(31205,31222) = 974282510 / 1
LCM(31205,31222) = 974282510

Least Common Multiple (LCM) of 31205 and 31222 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31205 and 31222. First we will calculate the prime factors of 31205 and 31222.

Prime Factorization of 31205

Prime factors of 31205 are 5, 79. Prime factorization of 31205 in exponential form is:

31205 = 51 × 792

Prime Factorization of 31222

Prime factors of 31222 are 2, 67, 233. Prime factorization of 31222 in exponential form is:

31222 = 21 × 671 × 2331

Now multiplying the highest exponent prime factors to calculate the LCM of 31205 and 31222.

LCM(31205,31222) = 51 × 792 × 21 × 671 × 2331
LCM(31205,31222) = 974282510