What is the Least Common Multiple of 387 and 405?
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 387 and 405 is 17415.
LCM(387,405) = 17415
Least Common Multiple of 387 and 405 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 387 and 405, than apply into the LCM equation.
GCF(387,405) = 9
LCM(387,405) = ( 387 × 405) / 9
LCM(387,405) = 156735 / 9
LCM(387,405) = 17415
Least Common Multiple (LCM) of 387 and 405 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 387 and 405. First we will calculate the prime factors of 387 and 405.
Prime Factorization of 387
Prime factors of 387 are 3, 43. Prime factorization of 387 in exponential form is:
387 = 32 × 431
Prime Factorization of 405
Prime factors of 405 are 3, 5. Prime factorization of 405 in exponential form is:
405 = 34 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 387 and 405.
LCM(387,405) = 34 × 431 × 51
LCM(387,405) = 17415
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