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What is the Least Common Multiple of 67743 and 67760?

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 67743 and 67760 is 4590265680.

LCM(67743,67760) = 4590265680

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Least Common Multiple of 67743 and 67760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67743 and 67760, than apply into the LCM equation.

GCF(67743,67760) = 1
LCM(67743,67760) = ( 67743 × 67760) / 1
LCM(67743,67760) = 4590265680 / 1
LCM(67743,67760) = 4590265680

Least Common Multiple (LCM) of 67743 and 67760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67743 and 67760. First we will calculate the prime factors of 67743 and 67760.

Prime Factorization of 67743

Prime factors of 67743 are 3, 13, 193. Prime factorization of 67743 in exponential form is:

67743 = 33 × 131 × 1931

Prime Factorization of 67760

Prime factors of 67760 are 2, 5, 7, 11. Prime factorization of 67760 in exponential form is:

67760 = 24 × 51 × 71 × 112

Now multiplying the highest exponent prime factors to calculate the LCM of 67743 and 67760.

LCM(67743,67760) = 33 × 131 × 1931 × 24 × 51 × 71 × 112
LCM(67743,67760) = 4590265680