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What is the Least Common Multiple of 16746 and 16752?

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 16746 and 16752 is 46754832.

LCM(16746,16752) = 46754832

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Least Common Multiple of 16746 and 16752 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16746 and 16752, than apply into the LCM equation.

GCF(16746,16752) = 6
LCM(16746,16752) = ( 16746 × 16752) / 6
LCM(16746,16752) = 280528992 / 6
LCM(16746,16752) = 46754832

Least Common Multiple (LCM) of 16746 and 16752 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 16746 and 16752. First we will calculate the prime factors of 16746 and 16752.

Prime Factorization of 16746

Prime factors of 16746 are 2, 3, 2791. Prime factorization of 16746 in exponential form is:

16746 = 21 × 31 × 27911

Prime Factorization of 16752

Prime factors of 16752 are 2, 3, 349. Prime factorization of 16752 in exponential form is:

16752 = 24 × 31 × 3491

Now multiplying the highest exponent prime factors to calculate the LCM of 16746 and 16752.

LCM(16746,16752) = 24 × 31 × 27911 × 3491
LCM(16746,16752) = 46754832