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What is the Least Common Multiple of 3782 and 3800?

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 3782 and 3800 is 7185800.

LCM(3782,3800) = 7185800

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Least Common Multiple of 3782 and 3800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3782 and 3800, than apply into the LCM equation.

GCF(3782,3800) = 2
LCM(3782,3800) = ( 3782 × 3800) / 2
LCM(3782,3800) = 14371600 / 2
LCM(3782,3800) = 7185800

Least Common Multiple (LCM) of 3782 and 3800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3782 and 3800. First we will calculate the prime factors of 3782 and 3800.

Prime Factorization of 3782

Prime factors of 3782 are 2, 31, 61. Prime factorization of 3782 in exponential form is:

3782 = 21 × 311 × 611

Prime Factorization of 3800

Prime factors of 3800 are 2, 5, 19. Prime factorization of 3800 in exponential form is:

3800 = 23 × 52 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 3782 and 3800.

LCM(3782,3800) = 23 × 311 × 611 × 52 × 191
LCM(3782,3800) = 7185800