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What is the Least Common Multiple of 13791 and 13800?

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 13791 and 13800 is 63438600.

LCM(13791,13800) = 63438600

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Least Common Multiple of 13791 and 13800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13791 and 13800, than apply into the LCM equation.

GCF(13791,13800) = 3
LCM(13791,13800) = ( 13791 × 13800) / 3
LCM(13791,13800) = 190315800 / 3
LCM(13791,13800) = 63438600

Least Common Multiple (LCM) of 13791 and 13800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13791 and 13800. First we will calculate the prime factors of 13791 and 13800.

Prime Factorization of 13791

Prime factors of 13791 are 3, 4597. Prime factorization of 13791 in exponential form is:

13791 = 31 × 45971

Prime Factorization of 13800

Prime factors of 13800 are 2, 3, 5, 23. Prime factorization of 13800 in exponential form is:

13800 = 23 × 31 × 52 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 13791 and 13800.

LCM(13791,13800) = 31 × 45971 × 23 × 52 × 231
LCM(13791,13800) = 63438600