What is the Least Common Multiple of 13689 and 13704?
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 13689 and 13704 is 62531352.
LCM(13689,13704) = 62531352
Least Common Multiple of 13689 and 13704 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13689 and 13704, than apply into the LCM equation.
GCF(13689,13704) = 3
LCM(13689,13704) = ( 13689 × 13704) / 3
LCM(13689,13704) = 187594056 / 3
LCM(13689,13704) = 62531352
Least Common Multiple (LCM) of 13689 and 13704 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13689 and 13704. First we will calculate the prime factors of 13689 and 13704.
Prime Factorization of 13689
Prime factors of 13689 are 3, 13. Prime factorization of 13689 in exponential form is:
13689 = 34 × 132
Prime Factorization of 13704
Prime factors of 13704 are 2, 3, 571. Prime factorization of 13704 in exponential form is:
13704 = 23 × 31 × 5711
Now multiplying the highest exponent prime factors to calculate the LCM of 13689 and 13704.
LCM(13689,13704) = 34 × 132 × 23 × 5711
LCM(13689,13704) = 62531352
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