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What is the Least Common Multiple of 32172 and 32192?

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 32172 and 32192 is 258920256.

LCM(32172,32192) = 258920256

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Least Common Multiple of 32172 and 32192 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32172 and 32192, than apply into the LCM equation.

GCF(32172,32192) = 4
LCM(32172,32192) = ( 32172 × 32192) / 4
LCM(32172,32192) = 1035681024 / 4
LCM(32172,32192) = 258920256

Least Common Multiple (LCM) of 32172 and 32192 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32172 and 32192. First we will calculate the prime factors of 32172 and 32192.

Prime Factorization of 32172

Prime factors of 32172 are 2, 3, 7, 383. Prime factorization of 32172 in exponential form is:

32172 = 22 × 31 × 71 × 3831

Prime Factorization of 32192

Prime factors of 32192 are 2, 503. Prime factorization of 32192 in exponential form is:

32192 = 26 × 5031

Now multiplying the highest exponent prime factors to calculate the LCM of 32172 and 32192.

LCM(32172,32192) = 26 × 31 × 71 × 3831 × 5031
LCM(32172,32192) = 258920256