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What is the Least Common Multiple of 67674 and 67684?

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 67674 and 67684 is 2290223508.

LCM(67674,67684) = 2290223508

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Least Common Multiple of 67674 and 67684 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67674 and 67684, than apply into the LCM equation.

GCF(67674,67684) = 2
LCM(67674,67684) = ( 67674 × 67684) / 2
LCM(67674,67684) = 4580447016 / 2
LCM(67674,67684) = 2290223508

Least Common Multiple (LCM) of 67674 and 67684 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67674 and 67684. First we will calculate the prime factors of 67674 and 67684.

Prime Factorization of 67674

Prime factors of 67674 are 2, 3, 11279. Prime factorization of 67674 in exponential form is:

67674 = 21 × 31 × 112791

Prime Factorization of 67684

Prime factors of 67684 are 2, 16921. Prime factorization of 67684 in exponential form is:

67684 = 22 × 169211

Now multiplying the highest exponent prime factors to calculate the LCM of 67674 and 67684.

LCM(67674,67684) = 22 × 31 × 112791 × 169211
LCM(67674,67684) = 2290223508