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What is the Least Common Multiple of 31075 and 31080?

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 31075 and 31080 is 193162200.

LCM(31075,31080) = 193162200

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Least Common Multiple of 31075 and 31080 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31075 and 31080, than apply into the LCM equation.

GCF(31075,31080) = 5
LCM(31075,31080) = ( 31075 × 31080) / 5
LCM(31075,31080) = 965811000 / 5
LCM(31075,31080) = 193162200

Least Common Multiple (LCM) of 31075 and 31080 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31075 and 31080. First we will calculate the prime factors of 31075 and 31080.

Prime Factorization of 31075

Prime factors of 31075 are 5, 11, 113. Prime factorization of 31075 in exponential form is:

31075 = 52 × 111 × 1131

Prime Factorization of 31080

Prime factors of 31080 are 2, 3, 5, 7, 37. Prime factorization of 31080 in exponential form is:

31080 = 23 × 31 × 51 × 71 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 31075 and 31080.

LCM(31075,31080) = 52 × 111 × 1131 × 23 × 31 × 71 × 371
LCM(31075,31080) = 193162200