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What is the Least Common Multiple of 31302 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 31302 and 31320 is 54465480.

LCM(31302,31320) = 54465480

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Least Common Multiple of 31302 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 31302 and 31320, than apply into the LCM equation.

GCF(31302,31320) = 18
LCM(31302,31320) = ( 31302 × 31320) / 18
LCM(31302,31320) = 980378640 / 18
LCM(31302,31320) = 54465480

Least Common Multiple (LCM) of 31302 and 31320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31302 and 31320. First we will calculate the prime factors of 31302 and 31320.

Prime Factorization of 31302

Prime factors of 31302 are 2, 3, 37, 47. Prime factorization of 31302 in exponential form is:

31302 = 21 × 32 × 371 × 471

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 31302 and 31320.

LCM(31302,31320) = 23 × 33 × 371 × 471 × 51 × 291
LCM(31302,31320) = 54465480