What is the Least Common Multiple of 413 and 417?
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 417 is 172221.
LCM(413,417) = 172221
Least Common Multiple of 413 and 417 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 417, than apply into the LCM equation.
GCF(413,417) = 1
LCM(413,417) = ( 413 × 417) / 1
LCM(413,417) = 172221 / 1
LCM(413,417) = 172221
Least Common Multiple (LCM) of 413 and 417 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 413 and 417. First we will calculate the prime factors of 413 and 417.
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 417
Prime factors of 417 are 3, 139. Prime factorization of 417 in exponential form is:
417 = 31 × 1391
Now multiplying the highest exponent prime factors to calculate the LCM of 413 and 417.
LCM(413,417) = 71 × 591 × 31 × 1391
LCM(413,417) = 172221
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