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What is the Least Common Multiple of 417 and 421?

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 417 and 421 is 175557.

LCM(417,421) = 175557

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Least Common Multiple of 417 and 421 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 417 and 421, than apply into the LCM equation.

GCF(417,421) = 1
LCM(417,421) = ( 417 × 421) / 1
LCM(417,421) = 175557 / 1
LCM(417,421) = 175557

Least Common Multiple (LCM) of 417 and 421 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 417 and 421. First we will calculate the prime factors of 417 and 421.

Prime Factorization of 417

Prime factors of 417 are 3, 139. Prime factorization of 417 in exponential form is:

417 = 31 × 1391

Prime Factorization of 421

Prime factors of 421 are 421. Prime factorization of 421 in exponential form is:

421 = 4211

Now multiplying the highest exponent prime factors to calculate the LCM of 417 and 421.

LCM(417,421) = 31 × 1391 × 4211
LCM(417,421) = 175557