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What is the Least Common Multiple of 169 and 188?

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 188 is 31772.

LCM(169,188) = 31772

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Least Common Multiple of 169 and 188 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 188, than apply into the LCM equation.

GCF(169,188) = 1
LCM(169,188) = ( 169 × 188) / 1
LCM(169,188) = 31772 / 1
LCM(169,188) = 31772

Least Common Multiple (LCM) of 169 and 188 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 169 and 188. First we will calculate the prime factors of 169 and 188.

Prime Factorization of 169

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

169 = 132

Prime Factorization of 188

Prime factors of 188 are 2, 47. Prime factorization of 188 in exponential form is:

188 = 22 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 169 and 188.

LCM(169,188) = 132 × 22 × 471
LCM(169,188) = 31772

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