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What is the Least Common Multiple of 13750 and 13760?

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 13750 and 13760 is 18920000.

LCM(13750,13760) = 18920000

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Least Common Multiple of 13750 and 13760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13750 and 13760, than apply into the LCM equation.

GCF(13750,13760) = 10
LCM(13750,13760) = ( 13750 × 13760) / 10
LCM(13750,13760) = 189200000 / 10
LCM(13750,13760) = 18920000

Least Common Multiple (LCM) of 13750 and 13760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13750 and 13760. First we will calculate the prime factors of 13750 and 13760.

Prime Factorization of 13750

Prime factors of 13750 are 2, 5, 11. Prime factorization of 13750 in exponential form is:

13750 = 21 × 54 × 111

Prime Factorization of 13760

Prime factors of 13760 are 2, 5, 43. Prime factorization of 13760 in exponential form is:

13760 = 26 × 51 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 13750 and 13760.

LCM(13750,13760) = 26 × 54 × 111 × 431
LCM(13750,13760) = 18920000