What is the Least Common Multiple of 285 and 299?
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 285 and 299 is 85215.
LCM(285,299) = 85215
Least Common Multiple of 285 and 299 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 285 and 299, than apply into the LCM equation.
GCF(285,299) = 1
LCM(285,299) = ( 285 × 299) / 1
LCM(285,299) = 85215 / 1
LCM(285,299) = 85215
Least Common Multiple (LCM) of 285 and 299 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 285 and 299. First we will calculate the prime factors of 285 and 299.
Prime Factorization of 285
Prime factors of 285 are 3, 5, 19. Prime factorization of 285 in exponential form is:
285 = 31 × 51 × 191
Prime Factorization of 299
Prime factors of 299 are 13, 23. Prime factorization of 299 in exponential form is:
299 = 131 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 285 and 299.
LCM(285,299) = 31 × 51 × 191 × 131 × 231
LCM(285,299) = 85215
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