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What is the Least Common Multiple of 31098 and 31110?

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 31098 and 31110 is 161243130.

LCM(31098,31110) = 161243130

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Least Common Multiple of 31098 and 31110 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31098 and 31110, than apply into the LCM equation.

GCF(31098,31110) = 6
LCM(31098,31110) = ( 31098 × 31110) / 6
LCM(31098,31110) = 967458780 / 6
LCM(31098,31110) = 161243130

Least Common Multiple (LCM) of 31098 and 31110 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31098 and 31110. First we will calculate the prime factors of 31098 and 31110.

Prime Factorization of 31098

Prime factors of 31098 are 2, 3, 71, 73. Prime factorization of 31098 in exponential form is:

31098 = 21 × 31 × 711 × 731

Prime Factorization of 31110

Prime factors of 31110 are 2, 3, 5, 17, 61. Prime factorization of 31110 in exponential form is:

31110 = 21 × 31 × 51 × 171 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 31098 and 31110.

LCM(31098,31110) = 21 × 31 × 711 × 731 × 51 × 171 × 611
LCM(31098,31110) = 161243130