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What is the Least Common Multiple of 31300 and 31320?

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 31300 and 31320 is 49015800.

LCM(31300,31320) = 49015800

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Least Common Multiple of 31300 and 31320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31300 and 31320, than apply into the LCM equation.

GCF(31300,31320) = 20
LCM(31300,31320) = ( 31300 × 31320) / 20
LCM(31300,31320) = 980316000 / 20
LCM(31300,31320) = 49015800

Least Common Multiple (LCM) of 31300 and 31320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31300 and 31320. First we will calculate the prime factors of 31300 and 31320.

Prime Factorization of 31300

Prime factors of 31300 are 2, 5, 313. Prime factorization of 31300 in exponential form is:

31300 = 22 × 52 × 3131

Prime Factorization of 31320

Prime factors of 31320 are 2, 3, 5, 29. Prime factorization of 31320 in exponential form is:

31320 = 23 × 33 × 51 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 31300 and 31320.

LCM(31300,31320) = 23 × 52 × 3131 × 33 × 291
LCM(31300,31320) = 49015800