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What is the Least Common Multiple of 53210 and 53214?

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 53210 and 53214 is 1415758470.

LCM(53210,53214) = 1415758470

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Least Common Multiple of 53210 and 53214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 53210 and 53214, than apply into the LCM equation.

GCF(53210,53214) = 2
LCM(53210,53214) = ( 53210 × 53214) / 2
LCM(53210,53214) = 2831516940 / 2
LCM(53210,53214) = 1415758470

Least Common Multiple (LCM) of 53210 and 53214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 53210 and 53214. First we will calculate the prime factors of 53210 and 53214.

Prime Factorization of 53210

Prime factors of 53210 are 2, 5, 17, 313. Prime factorization of 53210 in exponential form is:

53210 = 21 × 51 × 171 × 3131

Prime Factorization of 53214

Prime factors of 53214 are 2, 3, 7, 181. Prime factorization of 53214 in exponential form is:

53214 = 21 × 31 × 72 × 1811

Now multiplying the highest exponent prime factors to calculate the LCM of 53210 and 53214.

LCM(53210,53214) = 21 × 51 × 171 × 3131 × 31 × 72 × 1811
LCM(53210,53214) = 1415758470