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What is the Least Common Multiple of 14 and 24?

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 14 and 24 is 168.

LCM(14,24) = 168

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Least Common Multiple of 14 and 24 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 24, than apply into the LCM equation.

GCF(14,24) = 2
LCM(14,24) = ( 14 × 24) / 2
LCM(14,24) = 336 / 2
LCM(14,24) = 168

Least Common Multiple (LCM) of 14 and 24 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 24. First we will calculate the prime factors of 14 and 24.

Prime Factorization of 14

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

14 = 21 × 71

Prime Factorization of 24

Prime factors of 24 are 2, 3. Prime factorization of 24 in exponential form is:

24 = 23 × 31

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 24.

LCM(14,24) = 23 × 71 × 31
LCM(14,24) = 168

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blake 2021-01-21 23:43:52

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