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What is the Least Common Multiple of 29856 and 29872?

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 29856 and 29872 is 55741152.

LCM(29856,29872) = 55741152

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Least Common Multiple of 29856 and 29872 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29856 and 29872, than apply into the LCM equation.

GCF(29856,29872) = 16
LCM(29856,29872) = ( 29856 × 29872) / 16
LCM(29856,29872) = 891858432 / 16
LCM(29856,29872) = 55741152

Least Common Multiple (LCM) of 29856 and 29872 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29856 and 29872. First we will calculate the prime factors of 29856 and 29872.

Prime Factorization of 29856

Prime factors of 29856 are 2, 3, 311. Prime factorization of 29856 in exponential form is:

29856 = 25 × 31 × 3111

Prime Factorization of 29872

Prime factors of 29872 are 2, 1867. Prime factorization of 29872 in exponential form is:

29872 = 24 × 18671

Now multiplying the highest exponent prime factors to calculate the LCM of 29856 and 29872.

LCM(29856,29872) = 25 × 31 × 3111 × 18671
LCM(29856,29872) = 55741152