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What is the Least Common Multiple of 417 and 435?

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 435 is 60465.

LCM(417,435) = 60465

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Least Common Multiple of 417 and 435 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 435, than apply into the LCM equation.

GCF(417,435) = 3
LCM(417,435) = ( 417 × 435) / 3
LCM(417,435) = 181395 / 3
LCM(417,435) = 60465

Least Common Multiple (LCM) of 417 and 435 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 417 and 435. First we will calculate the prime factors of 417 and 435.

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 435

Prime factors of 435 are 3, 5, 29. Prime factorization of 435 in exponential form is:

435 = 31 × 51 × 291

Now multiplying the highest exponent prime factors to calculate the LCM of 417 and 435.

LCM(417,435) = 31 × 1391 × 51 × 291
LCM(417,435) = 60465