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What is the Least Common Multiple of 29752 and 29760?

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 29752 and 29760 is 110677440.

LCM(29752,29760) = 110677440

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Least Common Multiple of 29752 and 29760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29752 and 29760, than apply into the LCM equation.

GCF(29752,29760) = 8
LCM(29752,29760) = ( 29752 × 29760) / 8
LCM(29752,29760) = 885419520 / 8
LCM(29752,29760) = 110677440

Least Common Multiple (LCM) of 29752 and 29760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29752 and 29760. First we will calculate the prime factors of 29752 and 29760.

Prime Factorization of 29752

Prime factors of 29752 are 2, 3719. Prime factorization of 29752 in exponential form is:

29752 = 23 × 37191

Prime Factorization of 29760

Prime factors of 29760 are 2, 3, 5, 31. Prime factorization of 29760 in exponential form is:

29760 = 26 × 31 × 51 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 29752 and 29760.

LCM(29752,29760) = 26 × 37191 × 31 × 51 × 311
LCM(29752,29760) = 110677440