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What is the Least Common Multiple of 5 and 14?

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 5 and 14 is 70.

LCM(5,14) = 70

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Least Common Multiple of 5 and 14 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 14, than apply into the LCM equation.

GCF(5,14) = 1
LCM(5,14) = ( 5 × 14) / 1
LCM(5,14) = 70 / 1
LCM(5,14) = 70

Least Common Multiple (LCM) of 5 and 14 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 14. First we will calculate the prime factors of 5 and 14.

Prime Factorization of 5

Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:

5 = 51

Prime Factorization of 14

Prime factors of 14 are 2, 7. Prime factorization of 14 in exponential form is:

14 = 21 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 14.

LCM(5,14) = 51 × 21 × 71
LCM(5,14) = 70

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