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What is the Least Common Multiple of 15684 and 15704?

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 15684 and 15704 is 61575384.

LCM(15684,15704) = 61575384

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Least Common Multiple of 15684 and 15704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15684 and 15704, than apply into the LCM equation.

GCF(15684,15704) = 4
LCM(15684,15704) = ( 15684 × 15704) / 4
LCM(15684,15704) = 246301536 / 4
LCM(15684,15704) = 61575384

Least Common Multiple (LCM) of 15684 and 15704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15684 and 15704. First we will calculate the prime factors of 15684 and 15704.

Prime Factorization of 15684

Prime factors of 15684 are 2, 3, 1307. Prime factorization of 15684 in exponential form is:

15684 = 22 × 31 × 13071

Prime Factorization of 15704

Prime factors of 15704 are 2, 13, 151. Prime factorization of 15704 in exponential form is:

15704 = 23 × 131 × 1511

Now multiplying the highest exponent prime factors to calculate the LCM of 15684 and 15704.

LCM(15684,15704) = 23 × 31 × 13071 × 131 × 1511
LCM(15684,15704) = 61575384