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What is the Least Common Multiple of 402 and 409?

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 402 and 409 is 164418.

LCM(402,409) = 164418

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Least Common Multiple of 402 and 409 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 402 and 409, than apply into the LCM equation.

GCF(402,409) = 1
LCM(402,409) = ( 402 × 409) / 1
LCM(402,409) = 164418 / 1
LCM(402,409) = 164418

Least Common Multiple (LCM) of 402 and 409 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 402 and 409. First we will calculate the prime factors of 402 and 409.

Prime Factorization of 402

Prime factors of 402 are 2, 3, 67. Prime factorization of 402 in exponential form is:

402 = 21 × 31 × 671

Prime Factorization of 409

Prime factors of 409 are 409. Prime factorization of 409 in exponential form is:

409 = 4091

Now multiplying the highest exponent prime factors to calculate the LCM of 402 and 409.

LCM(402,409) = 21 × 31 × 671 × 4091
LCM(402,409) = 164418