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What is the Least Common Multiple of 30338 and 30352?

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 30338 and 30352 is 65772784.

LCM(30338,30352) = 65772784

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Least Common Multiple of 30338 and 30352 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30338 and 30352, than apply into the LCM equation.

GCF(30338,30352) = 14
LCM(30338,30352) = ( 30338 × 30352) / 14
LCM(30338,30352) = 920818976 / 14
LCM(30338,30352) = 65772784

Least Common Multiple (LCM) of 30338 and 30352 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30338 and 30352. First we will calculate the prime factors of 30338 and 30352.

Prime Factorization of 30338

Prime factors of 30338 are 2, 7, 11, 197. Prime factorization of 30338 in exponential form is:

30338 = 21 × 71 × 111 × 1971

Prime Factorization of 30352

Prime factors of 30352 are 2, 7, 271. Prime factorization of 30352 in exponential form is:

30352 = 24 × 71 × 2711

Now multiplying the highest exponent prime factors to calculate the LCM of 30338 and 30352.

LCM(30338,30352) = 24 × 71 × 111 × 1971 × 2711
LCM(30338,30352) = 65772784