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What is the Least Common Multiple of 13135 and 13140?

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 13135 and 13140 is 34518780.

LCM(13135,13140) = 34518780

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Least Common Multiple of 13135 and 13140 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13135 and 13140, than apply into the LCM equation.

GCF(13135,13140) = 5
LCM(13135,13140) = ( 13135 × 13140) / 5
LCM(13135,13140) = 172593900 / 5
LCM(13135,13140) = 34518780

Least Common Multiple (LCM) of 13135 and 13140 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13135 and 13140. First we will calculate the prime factors of 13135 and 13140.

Prime Factorization of 13135

Prime factors of 13135 are 5, 37, 71. Prime factorization of 13135 in exponential form is:

13135 = 51 × 371 × 711

Prime Factorization of 13140

Prime factors of 13140 are 2, 3, 5, 73. Prime factorization of 13140 in exponential form is:

13140 = 22 × 32 × 51 × 731

Now multiplying the highest exponent prime factors to calculate the LCM of 13135 and 13140.

LCM(13135,13140) = 51 × 371 × 711 × 22 × 32 × 731
LCM(13135,13140) = 34518780