What is the Least Common Multiple of 13702 and 13717?
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 13702 and 13717 is 187950334.
LCM(13702,13717) = 187950334
Least Common Multiple of 13702 and 13717 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13702 and 13717, than apply into the LCM equation.
GCF(13702,13717) = 1
LCM(13702,13717) = ( 13702 × 13717) / 1
LCM(13702,13717) = 187950334 / 1
LCM(13702,13717) = 187950334
Least Common Multiple (LCM) of 13702 and 13717 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13702 and 13717. First we will calculate the prime factors of 13702 and 13717.
Prime Factorization of 13702
Prime factors of 13702 are 2, 13, 17, 31. Prime factorization of 13702 in exponential form is:
13702 = 21 × 131 × 171 × 311
Prime Factorization of 13717
Prime factors of 13717 are 11, 29, 43. Prime factorization of 13717 in exponential form is:
13717 = 111 × 291 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 13702 and 13717.
LCM(13702,13717) = 21 × 131 × 171 × 311 × 111 × 291 × 431
LCM(13702,13717) = 187950334
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