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What is the Least Common Multiple of 169 and 178?

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 178 is 30082.

LCM(169,178) = 30082

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Least Common Multiple of 169 and 178 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 178, than apply into the LCM equation.

GCF(169,178) = 1
LCM(169,178) = ( 169 × 178) / 1
LCM(169,178) = 30082 / 1
LCM(169,178) = 30082

Least Common Multiple (LCM) of 169 and 178 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 169 and 178. First we will calculate the prime factors of 169 and 178.

Prime Factorization of 169

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

169 = 132

Prime Factorization of 178

Prime factors of 178 are 2, 89. Prime factorization of 178 in exponential form is:

178 = 21 × 891

Now multiplying the highest exponent prime factors to calculate the LCM of 169 and 178.

LCM(169,178) = 132 × 21 × 891
LCM(169,178) = 30082

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