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What is the Least Common Multiple of 7692 and 7710?

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 7692 and 7710 is 9884220.

LCM(7692,7710) = 9884220

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Least Common Multiple of 7692 and 7710 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7692 and 7710, than apply into the LCM equation.

GCF(7692,7710) = 6
LCM(7692,7710) = ( 7692 × 7710) / 6
LCM(7692,7710) = 59305320 / 6
LCM(7692,7710) = 9884220

Least Common Multiple (LCM) of 7692 and 7710 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7692 and 7710. First we will calculate the prime factors of 7692 and 7710.

Prime Factorization of 7692

Prime factors of 7692 are 2, 3, 641. Prime factorization of 7692 in exponential form is:

7692 = 22 × 31 × 6411

Prime Factorization of 7710

Prime factors of 7710 are 2, 3, 5, 257. Prime factorization of 7710 in exponential form is:

7710 = 21 × 31 × 51 × 2571

Now multiplying the highest exponent prime factors to calculate the LCM of 7692 and 7710.

LCM(7692,7710) = 22 × 31 × 6411 × 51 × 2571
LCM(7692,7710) = 9884220