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What is the Least Common Multiple of 46305 and 46315?

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 46305 and 46315 is 428923215.

LCM(46305,46315) = 428923215

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Least Common Multiple of 46305 and 46315 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46305 and 46315, than apply into the LCM equation.

GCF(46305,46315) = 5
LCM(46305,46315) = ( 46305 × 46315) / 5
LCM(46305,46315) = 2144616075 / 5
LCM(46305,46315) = 428923215

Least Common Multiple (LCM) of 46305 and 46315 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46305 and 46315. First we will calculate the prime factors of 46305 and 46315.

Prime Factorization of 46305

Prime factors of 46305 are 3, 5, 7. Prime factorization of 46305 in exponential form is:

46305 = 33 × 51 × 73

Prime Factorization of 46315

Prime factors of 46315 are 5, 59, 157. Prime factorization of 46315 in exponential form is:

46315 = 51 × 591 × 1571

Now multiplying the highest exponent prime factors to calculate the LCM of 46305 and 46315.

LCM(46305,46315) = 33 × 51 × 73 × 591 × 1571
LCM(46305,46315) = 428923215