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What is the Least Common Multiple of 27414 and 27420?

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 27414 and 27420 is 125281980.

LCM(27414,27420) = 125281980

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Least Common Multiple of 27414 and 27420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27414 and 27420, than apply into the LCM equation.

GCF(27414,27420) = 6
LCM(27414,27420) = ( 27414 × 27420) / 6
LCM(27414,27420) = 751691880 / 6
LCM(27414,27420) = 125281980

Least Common Multiple (LCM) of 27414 and 27420 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27414 and 27420. First we will calculate the prime factors of 27414 and 27420.

Prime Factorization of 27414

Prime factors of 27414 are 2, 3, 1523. Prime factorization of 27414 in exponential form is:

27414 = 21 × 32 × 15231

Prime Factorization of 27420

Prime factors of 27420 are 2, 3, 5, 457. Prime factorization of 27420 in exponential form is:

27420 = 22 × 31 × 51 × 4571

Now multiplying the highest exponent prime factors to calculate the LCM of 27414 and 27420.

LCM(27414,27420) = 22 × 32 × 15231 × 51 × 4571
LCM(27414,27420) = 125281980