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What is the Least Common Multiple of 13716 and 13722?

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 13716 and 13722 is 31368492.

LCM(13716,13722) = 31368492

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Least Common Multiple of 13716 and 13722 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13716 and 13722, than apply into the LCM equation.

GCF(13716,13722) = 6
LCM(13716,13722) = ( 13716 × 13722) / 6
LCM(13716,13722) = 188210952 / 6
LCM(13716,13722) = 31368492

Least Common Multiple (LCM) of 13716 and 13722 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13716 and 13722. First we will calculate the prime factors of 13716 and 13722.

Prime Factorization of 13716

Prime factors of 13716 are 2, 3, 127. Prime factorization of 13716 in exponential form is:

13716 = 22 × 33 × 1271

Prime Factorization of 13722

Prime factors of 13722 are 2, 3, 2287. Prime factorization of 13722 in exponential form is:

13722 = 21 × 31 × 22871

Now multiplying the highest exponent prime factors to calculate the LCM of 13716 and 13722.

LCM(13716,13722) = 22 × 33 × 1271 × 22871
LCM(13716,13722) = 31368492