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What is the Least Common Multiple of 54270 and 54288?

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 54270 and 54288 is 163678320.

LCM(54270,54288) = 163678320

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Least Common Multiple of 54270 and 54288 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54270 and 54288, than apply into the LCM equation.

GCF(54270,54288) = 18
LCM(54270,54288) = ( 54270 × 54288) / 18
LCM(54270,54288) = 2946209760 / 18
LCM(54270,54288) = 163678320

Least Common Multiple (LCM) of 54270 and 54288 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54270 and 54288. First we will calculate the prime factors of 54270 and 54288.

Prime Factorization of 54270

Prime factors of 54270 are 2, 3, 5, 67. Prime factorization of 54270 in exponential form is:

54270 = 21 × 34 × 51 × 671

Prime Factorization of 54288

Prime factors of 54288 are 2, 3, 13, 29. Prime factorization of 54288 in exponential form is:

54288 = 24 × 32 × 131 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 54270 and 54288.

LCM(54270,54288) = 24 × 34 × 51 × 671 × 131 × 291
LCM(54270,54288) = 163678320