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What is the Least Common Multiple of 336 and 342?

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 336 and 342 is 19152.

LCM(336,342) = 19152

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Least Common Multiple of 336 and 342 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 336 and 342, than apply into the LCM equation.

GCF(336,342) = 6
LCM(336,342) = ( 336 × 342) / 6
LCM(336,342) = 114912 / 6
LCM(336,342) = 19152

Least Common Multiple (LCM) of 336 and 342 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 336 and 342. First we will calculate the prime factors of 336 and 342.

Prime Factorization of 336

Prime factors of 336 are 2, 3, 7. Prime factorization of 336 in exponential form is:

336 = 24 × 31 × 71

Prime Factorization of 342

Prime factors of 342 are 2, 3, 19. Prime factorization of 342 in exponential form is:

342 = 21 × 32 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 336 and 342.

LCM(336,342) = 24 × 32 × 71 × 191
LCM(336,342) = 19152