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What is the Least Common Multiple of 169 and 180?

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 169 and 180 is 30420.

LCM(169,180) = 30420

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Least Common Multiple of 169 and 180 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 169 and 180, than apply into the LCM equation.

GCF(169,180) = 1
LCM(169,180) = ( 169 × 180) / 1
LCM(169,180) = 30420 / 1
LCM(169,180) = 30420

Least Common Multiple (LCM) of 169 and 180 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 169 and 180. First we will calculate the prime factors of 169 and 180.

Prime Factorization of 169

Prime factors of 169 are 13. Prime factorization of 169 in exponential form is:

169 = 132

Prime Factorization of 180

Prime factors of 180 are 2, 3, 5. Prime factorization of 180 in exponential form is:

180 = 22 × 32 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 169 and 180.

LCM(169,180) = 132 × 22 × 32 × 51
LCM(169,180) = 30420

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