What is the Least Common Multiple of 13695 and 13710?
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 13695 and 13710 is 12517230.
LCM(13695,13710) = 12517230
Least Common Multiple of 13695 and 13710 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13695 and 13710, than apply into the LCM equation.
GCF(13695,13710) = 15
LCM(13695,13710) = ( 13695 × 13710) / 15
LCM(13695,13710) = 187758450 / 15
LCM(13695,13710) = 12517230
Least Common Multiple (LCM) of 13695 and 13710 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13695 and 13710. First we will calculate the prime factors of 13695 and 13710.
Prime Factorization of 13695
Prime factors of 13695 are 3, 5, 11, 83. Prime factorization of 13695 in exponential form is:
13695 = 31 × 51 × 111 × 831
Prime Factorization of 13710
Prime factors of 13710 are 2, 3, 5, 457. Prime factorization of 13710 in exponential form is:
13710 = 21 × 31 × 51 × 4571
Now multiplying the highest exponent prime factors to calculate the LCM of 13695 and 13710.
LCM(13695,13710) = 31 × 51 × 111 × 831 × 21 × 4571
LCM(13695,13710) = 12517230
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