What is the Least Common Multiple of 714 and 731?
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 714 and 731 is 30702.
LCM(714,731) = 30702
Least Common Multiple of 714 and 731 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 714 and 731, than apply into the LCM equation.
GCF(714,731) = 17
LCM(714,731) = ( 714 × 731) / 17
LCM(714,731) = 521934 / 17
LCM(714,731) = 30702
Least Common Multiple (LCM) of 714 and 731 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 714 and 731. First we will calculate the prime factors of 714 and 731.
Prime Factorization of 714
Prime factors of 714 are 2, 3, 7, 17. Prime factorization of 714 in exponential form is:
714 = 21 × 31 × 71 × 171
Prime Factorization of 731
Prime factors of 731 are 17, 43. Prime factorization of 731 in exponential form is:
731 = 171 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 714 and 731.
LCM(714,731) = 21 × 31 × 71 × 171 × 431
LCM(714,731) = 30702
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