What is the Least Common Multiple of 406 and 419?
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 406 and 419 is 170114.
LCM(406,419) = 170114
Least Common Multiple of 406 and 419 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 406 and 419, than apply into the LCM equation.
GCF(406,419) = 1
LCM(406,419) = ( 406 × 419) / 1
LCM(406,419) = 170114 / 1
LCM(406,419) = 170114
Least Common Multiple (LCM) of 406 and 419 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 406 and 419. First we will calculate the prime factors of 406 and 419.
Prime Factorization of 406
Prime factors of 406 are 2, 7, 29. Prime factorization of 406 in exponential form is:
406 = 21 × 71 × 291
Prime Factorization of 419
Prime factors of 419 are 419. Prime factorization of 419 in exponential form is:
419 = 4191
Now multiplying the highest exponent prime factors to calculate the LCM of 406 and 419.
LCM(406,419) = 21 × 71 × 291 × 4191
LCM(406,419) = 170114
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