What is the Least Common Multiple of 714 and 720?
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 720 is 85680.
LCM(714,720) = 85680
Least Common Multiple of 714 and 720 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 720, than apply into the LCM equation.
GCF(714,720) = 6
LCM(714,720) = ( 714 × 720) / 6
LCM(714,720) = 514080 / 6
LCM(714,720) = 85680
Least Common Multiple (LCM) of 714 and 720 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 714 and 720. First we will calculate the prime factors of 714 and 720.
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 720
Prime factors of 720 are 2, 3, 5. Prime factorization of 720 in exponential form is:
720 = 24 × 32 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 714 and 720.
LCM(714,720) = 24 × 32 × 71 × 171 × 51
LCM(714,720) = 85680
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