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What is the Least Common Multiple of 13695 and 13706?

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 13695 and 13706 is 17063970.

LCM(13695,13706) = 17063970

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Least Common Multiple of 13695 and 13706 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13695 and 13706, than apply into the LCM equation.

GCF(13695,13706) = 11
LCM(13695,13706) = ( 13695 × 13706) / 11
LCM(13695,13706) = 187703670 / 11
LCM(13695,13706) = 17063970

Least Common Multiple (LCM) of 13695 and 13706 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13695 and 13706. First we will calculate the prime factors of 13695 and 13706.

Prime Factorization of 13695

Prime factors of 13695 are 3, 5, 11, 83. Prime factorization of 13695 in exponential form is:

13695 = 31 × 51 × 111 × 831

Prime Factorization of 13706

Prime factors of 13706 are 2, 7, 11, 89. Prime factorization of 13706 in exponential form is:

13706 = 21 × 71 × 111 × 891

Now multiplying the highest exponent prime factors to calculate the LCM of 13695 and 13706.

LCM(13695,13706) = 31 × 51 × 111 × 831 × 21 × 71 × 891
LCM(13695,13706) = 17063970