What is the Least Common Multiple of 405 and 414?
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 405 and 414 is 18630.
LCM(405,414) = 18630
Least Common Multiple of 405 and 414 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 405 and 414, than apply into the LCM equation.
GCF(405,414) = 9
LCM(405,414) = ( 405 × 414) / 9
LCM(405,414) = 167670 / 9
LCM(405,414) = 18630
Least Common Multiple (LCM) of 405 and 414 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 405 and 414. First we will calculate the prime factors of 405 and 414.
Prime Factorization of 405
Prime factors of 405 are 3, 5. Prime factorization of 405 in exponential form is:
405 = 34 × 51
Prime Factorization of 414
Prime factors of 414 are 2, 3, 23. Prime factorization of 414 in exponential form is:
414 = 21 × 32 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 405 and 414.
LCM(405,414) = 34 × 51 × 21 × 231
LCM(405,414) = 18630
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