What is the Least Common Multiple of 413 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 413 and 419 is 173047.
LCM(413,419) = 173047
Least Common Multiple of 413 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 413 and 419, than apply into the LCM equation.
GCF(413,419) = 1
LCM(413,419) = ( 413 × 419) / 1
LCM(413,419) = 173047 / 1
LCM(413,419) = 173047
Least Common Multiple (LCM) of 413 and 419 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 413 and 419. First we will calculate the prime factors of 413 and 419.
Prime Factorization of 413
Prime factors of 413 are 7, 59. Prime factorization of 413 in exponential form is:
413 = 71 × 591
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 413 and 419.
LCM(413,419) = 71 × 591 × 4191
LCM(413,419) = 173047
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