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What is the Least Common Multiple of 29880 and 29888?

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 29880 and 29888 is 111631680.

LCM(29880,29888) = 111631680

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Least Common Multiple of 29880 and 29888 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29880 and 29888, than apply into the LCM equation.

GCF(29880,29888) = 8
LCM(29880,29888) = ( 29880 × 29888) / 8
LCM(29880,29888) = 893053440 / 8
LCM(29880,29888) = 111631680

Least Common Multiple (LCM) of 29880 and 29888 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29880 and 29888. First we will calculate the prime factors of 29880 and 29888.

Prime Factorization of 29880

Prime factors of 29880 are 2, 3, 5, 83. Prime factorization of 29880 in exponential form is:

29880 = 23 × 32 × 51 × 831

Prime Factorization of 29888

Prime factors of 29888 are 2, 467. Prime factorization of 29888 in exponential form is:

29888 = 26 × 4671

Now multiplying the highest exponent prime factors to calculate the LCM of 29880 and 29888.

LCM(29880,29888) = 26 × 32 × 51 × 831 × 4671
LCM(29880,29888) = 111631680