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What is the Least Common Multiple of 55302 and 55314?

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 55302 and 55314 is 509829138.

LCM(55302,55314) = 509829138

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Least Common Multiple of 55302 and 55314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55302 and 55314, than apply into the LCM equation.

GCF(55302,55314) = 6
LCM(55302,55314) = ( 55302 × 55314) / 6
LCM(55302,55314) = 3058974828 / 6
LCM(55302,55314) = 509829138

Least Common Multiple (LCM) of 55302 and 55314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55302 and 55314. First we will calculate the prime factors of 55302 and 55314.

Prime Factorization of 55302

Prime factors of 55302 are 2, 3, 13, 709. Prime factorization of 55302 in exponential form is:

55302 = 21 × 31 × 131 × 7091

Prime Factorization of 55314

Prime factors of 55314 are 2, 3, 7, 439. Prime factorization of 55314 in exponential form is:

55314 = 21 × 32 × 71 × 4391

Now multiplying the highest exponent prime factors to calculate the LCM of 55302 and 55314.

LCM(55302,55314) = 21 × 32 × 131 × 7091 × 71 × 4391
LCM(55302,55314) = 509829138