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What is the Least Common Multiple of 38304 and 38324?

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 38304 and 38324 is 366990624.

LCM(38304,38324) = 366990624

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Least Common Multiple of 38304 and 38324 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38304 and 38324, than apply into the LCM equation.

GCF(38304,38324) = 4
LCM(38304,38324) = ( 38304 × 38324) / 4
LCM(38304,38324) = 1467962496 / 4
LCM(38304,38324) = 366990624

Least Common Multiple (LCM) of 38304 and 38324 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38304 and 38324. First we will calculate the prime factors of 38304 and 38324.

Prime Factorization of 38304

Prime factors of 38304 are 2, 3, 7, 19. Prime factorization of 38304 in exponential form is:

38304 = 25 × 32 × 71 × 191

Prime Factorization of 38324

Prime factors of 38324 are 2, 11, 13, 67. Prime factorization of 38324 in exponential form is:

38324 = 22 × 111 × 131 × 671

Now multiplying the highest exponent prime factors to calculate the LCM of 38304 and 38324.

LCM(38304,38324) = 25 × 32 × 71 × 191 × 111 × 131 × 671
LCM(38304,38324) = 366990624