What is the Least Common Multiple of 13710 and 13714?
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 13710 and 13714 is 94009470.
LCM(13710,13714) = 94009470
Least Common Multiple of 13710 and 13714 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13710 and 13714, than apply into the LCM equation.
GCF(13710,13714) = 2
LCM(13710,13714) = ( 13710 × 13714) / 2
LCM(13710,13714) = 188018940 / 2
LCM(13710,13714) = 94009470
Least Common Multiple (LCM) of 13710 and 13714 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 13710 and 13714. First we will calculate the prime factors of 13710 and 13714.
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
Prime Factorization of 13714
Prime factors of 13714 are 2, 6857. Prime factorization of 13714 in exponential form is:
13714 = 21 × 68571
Now multiplying the highest exponent prime factors to calculate the LCM of 13710 and 13714.
LCM(13710,13714) = 21 × 31 × 51 × 4571 × 68571
LCM(13710,13714) = 94009470
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