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What is the Least Common Multiple of 14742 and 14752?

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 14742 and 14752 is 108736992.

LCM(14742,14752) = 108736992

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Least Common Multiple of 14742 and 14752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14742 and 14752, than apply into the LCM equation.

GCF(14742,14752) = 2
LCM(14742,14752) = ( 14742 × 14752) / 2
LCM(14742,14752) = 217473984 / 2
LCM(14742,14752) = 108736992

Least Common Multiple (LCM) of 14742 and 14752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 14742 and 14752. First we will calculate the prime factors of 14742 and 14752.

Prime Factorization of 14742

Prime factors of 14742 are 2, 3, 7, 13. Prime factorization of 14742 in exponential form is:

14742 = 21 × 34 × 71 × 131

Prime Factorization of 14752

Prime factors of 14752 are 2, 461. Prime factorization of 14752 in exponential form is:

14752 = 25 × 4611

Now multiplying the highest exponent prime factors to calculate the LCM of 14742 and 14752.

LCM(14742,14752) = 25 × 34 × 71 × 131 × 4611
LCM(14742,14752) = 108736992