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What is the Least Common Multiple of 13780 and 13784?

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 13780 and 13784 is 47485880.

LCM(13780,13784) = 47485880

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Least Common Multiple of 13780 and 13784 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13780 and 13784, than apply into the LCM equation.

GCF(13780,13784) = 4
LCM(13780,13784) = ( 13780 × 13784) / 4
LCM(13780,13784) = 189943520 / 4
LCM(13780,13784) = 47485880

Least Common Multiple (LCM) of 13780 and 13784 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13780 and 13784. First we will calculate the prime factors of 13780 and 13784.

Prime Factorization of 13780

Prime factors of 13780 are 2, 5, 13, 53. Prime factorization of 13780 in exponential form is:

13780 = 22 × 51 × 131 × 531

Prime Factorization of 13784

Prime factors of 13784 are 2, 1723. Prime factorization of 13784 in exponential form is:

13784 = 23 × 17231

Now multiplying the highest exponent prime factors to calculate the LCM of 13780 and 13784.

LCM(13780,13784) = 23 × 51 × 131 × 531 × 17231
LCM(13780,13784) = 47485880