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What is the Least Common Multiple of 69372 and 69384?

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 69372 and 69384 is 401108904.

LCM(69372,69384) = 401108904

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Least Common Multiple of 69372 and 69384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69372 and 69384, than apply into the LCM equation.

GCF(69372,69384) = 12
LCM(69372,69384) = ( 69372 × 69384) / 12
LCM(69372,69384) = 4813306848 / 12
LCM(69372,69384) = 401108904

Least Common Multiple (LCM) of 69372 and 69384 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69372 and 69384. First we will calculate the prime factors of 69372 and 69384.

Prime Factorization of 69372

Prime factors of 69372 are 2, 3, 41, 47. Prime factorization of 69372 in exponential form is:

69372 = 22 × 32 × 411 × 471

Prime Factorization of 69384

Prime factors of 69384 are 2, 3, 7, 59. Prime factorization of 69384 in exponential form is:

69384 = 23 × 31 × 72 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 69372 and 69384.

LCM(69372,69384) = 23 × 32 × 411 × 471 × 72 × 591
LCM(69372,69384) = 401108904