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What is the Least Common Multiple of 6762 and 6768?

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 6762 and 6768 is 7627536.

LCM(6762,6768) = 7627536

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Least Common Multiple of 6762 and 6768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6762 and 6768, than apply into the LCM equation.

GCF(6762,6768) = 6
LCM(6762,6768) = ( 6762 × 6768) / 6
LCM(6762,6768) = 45765216 / 6
LCM(6762,6768) = 7627536

Least Common Multiple (LCM) of 6762 and 6768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 6762 and 6768. First we will calculate the prime factors of 6762 and 6768.

Prime Factorization of 6762

Prime factors of 6762 are 2, 3, 7, 23. Prime factorization of 6762 in exponential form is:

6762 = 21 × 31 × 72 × 231

Prime Factorization of 6768

Prime factors of 6768 are 2, 3, 47. Prime factorization of 6768 in exponential form is:

6768 = 24 × 32 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 6762 and 6768.

LCM(6762,6768) = 24 × 32 × 72 × 231 × 471
LCM(6762,6768) = 7627536