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What is the Least Common Multiple of 67746 and 67764?

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 67746 and 67764 is 765123324.

LCM(67746,67764) = 765123324

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Least Common Multiple of 67746 and 67764 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67746 and 67764, than apply into the LCM equation.

GCF(67746,67764) = 6
LCM(67746,67764) = ( 67746 × 67764) / 6
LCM(67746,67764) = 4590739944 / 6
LCM(67746,67764) = 765123324

Least Common Multiple (LCM) of 67746 and 67764 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67746 and 67764. First we will calculate the prime factors of 67746 and 67764.

Prime Factorization of 67746

Prime factors of 67746 are 2, 3, 7, 1613. Prime factorization of 67746 in exponential form is:

67746 = 21 × 31 × 71 × 16131

Prime Factorization of 67764

Prime factors of 67764 are 2, 3, 5647. Prime factorization of 67764 in exponential form is:

67764 = 22 × 31 × 56471

Now multiplying the highest exponent prime factors to calculate the LCM of 67746 and 67764.

LCM(67746,67764) = 22 × 31 × 71 × 16131 × 56471
LCM(67746,67764) = 765123324