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What is the Least Common Multiple of 13475 and 13485?

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 13475 and 13485 is 36342075.

LCM(13475,13485) = 36342075

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Least Common Multiple of 13475 and 13485 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13475 and 13485, than apply into the LCM equation.

GCF(13475,13485) = 5
LCM(13475,13485) = ( 13475 × 13485) / 5
LCM(13475,13485) = 181710375 / 5
LCM(13475,13485) = 36342075

Least Common Multiple (LCM) of 13475 and 13485 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13475 and 13485. First we will calculate the prime factors of 13475 and 13485.

Prime Factorization of 13475

Prime factors of 13475 are 5, 7, 11. Prime factorization of 13475 in exponential form is:

13475 = 52 × 72 × 111

Prime Factorization of 13485

Prime factors of 13485 are 3, 5, 29, 31. Prime factorization of 13485 in exponential form is:

13485 = 31 × 51 × 291 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 13475 and 13485.

LCM(13475,13485) = 52 × 72 × 111 × 31 × 291 × 311
LCM(13475,13485) = 36342075