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Least Common Multiple of 14 and 32

Least common multiple (LCM) of 14 and 32 is 224.

LCM(14,32) = 224

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.

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Least Common Multiple of 14 and 32 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 32, than apply into the LCM equation.

GCF(14,32) = 2
LCM(14,32) = ( 14 × 32) / 2
LCM(14,32) = 448 / 2
LCM(14,32) = 224

Least Common Multiple (LCM) of 14 and 32 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 32. First we will calculate the prime factors of 14 and 32.

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 32

Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:

32 = 25

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 32.

LCM(14,32) = 25 × 71
LCM(14,32) = 224

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