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What is the Least Common Multiple of 67698 and 67704?

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 67698 and 67704 is 763904232.

LCM(67698,67704) = 763904232

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Least Common Multiple of 67698 and 67704 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67698 and 67704, than apply into the LCM equation.

GCF(67698,67704) = 6
LCM(67698,67704) = ( 67698 × 67704) / 6
LCM(67698,67704) = 4583425392 / 6
LCM(67698,67704) = 763904232

Least Common Multiple (LCM) of 67698 and 67704 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67698 and 67704. First we will calculate the prime factors of 67698 and 67704.

Prime Factorization of 67698

Prime factors of 67698 are 2, 3, 3761. Prime factorization of 67698 in exponential form is:

67698 = 21 × 32 × 37611

Prime Factorization of 67704

Prime factors of 67704 are 2, 3, 7, 13, 31. Prime factorization of 67704 in exponential form is:

67704 = 23 × 31 × 71 × 131 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 67698 and 67704.

LCM(67698,67704) = 23 × 32 × 37611 × 71 × 131 × 311
LCM(67698,67704) = 763904232