What is the Least Common Multiple of 67854 and 67864?
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 67854 and 67864 is 2302421928.
LCM(67854,67864) = 2302421928
Least Common Multiple of 67854 and 67864 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67854 and 67864, than apply into the LCM equation.
GCF(67854,67864) = 2
LCM(67854,67864) = ( 67854 × 67864) / 2
LCM(67854,67864) = 4604843856 / 2
LCM(67854,67864) = 2302421928
Least Common Multiple (LCM) of 67854 and 67864 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 67854 and 67864. First we will calculate the prime factors of 67854 and 67864.
Prime Factorization of 67854
Prime factors of 67854 are 2, 3, 43, 263. Prime factorization of 67854 in exponential form is:
67854 = 21 × 31 × 431 × 2631
Prime Factorization of 67864
Prime factors of 67864 are 2, 17, 499. Prime factorization of 67864 in exponential form is:
67864 = 23 × 171 × 4991
Now multiplying the highest exponent prime factors to calculate the LCM of 67854 and 67864.
LCM(67854,67864) = 23 × 31 × 431 × 2631 × 171 × 4991
LCM(67854,67864) = 2302421928
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