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What is the Least Common Multiple of 65300 and 65310?

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 65300 and 65310 is 426474300.

LCM(65300,65310) = 426474300

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Least Common Multiple of 65300 and 65310 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65300 and 65310, than apply into the LCM equation.

GCF(65300,65310) = 10
LCM(65300,65310) = ( 65300 × 65310) / 10
LCM(65300,65310) = 4264743000 / 10
LCM(65300,65310) = 426474300

Least Common Multiple (LCM) of 65300 and 65310 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65300 and 65310. First we will calculate the prime factors of 65300 and 65310.

Prime Factorization of 65300

Prime factors of 65300 are 2, 5, 653. Prime factorization of 65300 in exponential form is:

65300 = 22 × 52 × 6531

Prime Factorization of 65310

Prime factors of 65310 are 2, 3, 5, 7, 311. Prime factorization of 65310 in exponential form is:

65310 = 21 × 31 × 51 × 71 × 3111

Now multiplying the highest exponent prime factors to calculate the LCM of 65300 and 65310.

LCM(65300,65310) = 22 × 52 × 6531 × 31 × 71 × 3111
LCM(65300,65310) = 426474300