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What is the Least Common Multiple of 46005 and 46023?

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 46005 and 46023 is 705762705.

LCM(46005,46023) = 705762705

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Least Common Multiple of 46005 and 46023 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46005 and 46023, than apply into the LCM equation.

GCF(46005,46023) = 3
LCM(46005,46023) = ( 46005 × 46023) / 3
LCM(46005,46023) = 2117288115 / 3
LCM(46005,46023) = 705762705

Least Common Multiple (LCM) of 46005 and 46023 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 46005 and 46023. First we will calculate the prime factors of 46005 and 46023.

Prime Factorization of 46005

Prime factors of 46005 are 3, 5, 3067. Prime factorization of 46005 in exponential form is:

46005 = 31 × 51 × 30671

Prime Factorization of 46023

Prime factors of 46023 are 3, 23, 29. Prime factorization of 46023 in exponential form is:

46023 = 31 × 232 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 46005 and 46023.

LCM(46005,46023) = 31 × 51 × 30671 × 232 × 291
LCM(46005,46023) = 705762705