What is the Least Common Multiple of 13734 and 13740?
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 13734 and 13740 is 31450860.
LCM(13734,13740) = 31450860
Least Common Multiple of 13734 and 13740 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13734 and 13740, than apply into the LCM equation.
GCF(13734,13740) = 6
LCM(13734,13740) = ( 13734 × 13740) / 6
LCM(13734,13740) = 188705160 / 6
LCM(13734,13740) = 31450860
Least Common Multiple (LCM) of 13734 and 13740 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13734 and 13740. First we will calculate the prime factors of 13734 and 13740.
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
Prime Factorization of 13740
Prime factors of 13740 are 2, 3, 5, 229. Prime factorization of 13740 in exponential form is:
13740 = 22 × 31 × 51 × 2291
Now multiplying the highest exponent prime factors to calculate the LCM of 13734 and 13740.
LCM(13734,13740) = 22 × 32 × 71 × 1091 × 51 × 2291
LCM(13734,13740) = 31450860
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Related Least Common Multiples of 13740
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