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What is the Least Common Multiple of 13760 and 13776?

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 13760 and 13776 is 11847360.

LCM(13760,13776) = 11847360

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Least Common Multiple of 13760 and 13776 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13760 and 13776, than apply into the LCM equation.

GCF(13760,13776) = 16
LCM(13760,13776) = ( 13760 × 13776) / 16
LCM(13760,13776) = 189557760 / 16
LCM(13760,13776) = 11847360

Least Common Multiple (LCM) of 13760 and 13776 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13760 and 13776. First we will calculate the prime factors of 13760 and 13776.

Prime Factorization of 13760

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

13760 = 26 × 51 × 431

Prime Factorization of 13776

Prime factors of 13776 are 2, 3, 7, 41. Prime factorization of 13776 in exponential form is:

13776 = 24 × 31 × 71 × 411

Now multiplying the highest exponent prime factors to calculate the LCM of 13760 and 13776.

LCM(13760,13776) = 26 × 51 × 431 × 31 × 71 × 411
LCM(13760,13776) = 11847360