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What is the Least Common Multiple of 13530 and 13548?

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 13530 and 13548 is 30550740.

LCM(13530,13548) = 30550740

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Least Common Multiple of 13530 and 13548 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13530 and 13548, than apply into the LCM equation.

GCF(13530,13548) = 6
LCM(13530,13548) = ( 13530 × 13548) / 6
LCM(13530,13548) = 183304440 / 6
LCM(13530,13548) = 30550740

Least Common Multiple (LCM) of 13530 and 13548 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13530 and 13548. First we will calculate the prime factors of 13530 and 13548.

Prime Factorization of 13530

Prime factors of 13530 are 2, 3, 5, 11, 41. Prime factorization of 13530 in exponential form is:

13530 = 21 × 31 × 51 × 111 × 411

Prime Factorization of 13548

Prime factors of 13548 are 2, 3, 1129. Prime factorization of 13548 in exponential form is:

13548 = 22 × 31 × 11291

Now multiplying the highest exponent prime factors to calculate the LCM of 13530 and 13548.

LCM(13530,13548) = 22 × 31 × 51 × 111 × 411 × 11291
LCM(13530,13548) = 30550740