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What is the Least Common Multiple of 27878 and 27888?

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 27878 and 27888 is 388730832.

LCM(27878,27888) = 388730832

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Least Common Multiple of 27878 and 27888 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27878 and 27888, than apply into the LCM equation.

GCF(27878,27888) = 2
LCM(27878,27888) = ( 27878 × 27888) / 2
LCM(27878,27888) = 777461664 / 2
LCM(27878,27888) = 388730832

Least Common Multiple (LCM) of 27878 and 27888 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27878 and 27888. First we will calculate the prime factors of 27878 and 27888.

Prime Factorization of 27878

Prime factors of 27878 are 2, 53, 263. Prime factorization of 27878 in exponential form is:

27878 = 21 × 531 × 2631

Prime Factorization of 27888

Prime factors of 27888 are 2, 3, 7, 83. Prime factorization of 27888 in exponential form is:

27888 = 24 × 31 × 71 × 831

Now multiplying the highest exponent prime factors to calculate the LCM of 27878 and 27888.

LCM(27878,27888) = 24 × 531 × 2631 × 31 × 71 × 831
LCM(27878,27888) = 388730832