What is the Least Common Multiple of 13715 and 13734?
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 13715 and 13734 is 188361810.
LCM(13715,13734) = 188361810
Least Common Multiple of 13715 and 13734 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13715 and 13734, than apply into the LCM equation.
GCF(13715,13734) = 1
LCM(13715,13734) = ( 13715 × 13734) / 1
LCM(13715,13734) = 188361810 / 1
LCM(13715,13734) = 188361810
Least Common Multiple (LCM) of 13715 and 13734 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13715 and 13734. First we will calculate the prime factors of 13715 and 13734.
Prime Factorization of 13715
Prime factors of 13715 are 5, 13, 211. Prime factorization of 13715 in exponential form is:
13715 = 51 × 131 × 2111
Prime Factorization of 13734
Prime factors of 13734 are 2, 3, 7, 109. Prime factorization of 13734 in exponential form is:
13734 = 21 × 32 × 71 × 1091
Now multiplying the highest exponent prime factors to calculate the LCM of 13715 and 13734.
LCM(13715,13734) = 51 × 131 × 2111 × 21 × 32 × 71 × 1091
LCM(13715,13734) = 188361810
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