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What is the Least Common Multiple of 67668 and 67680?

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 67668 and 67680 is 381647520.

LCM(67668,67680) = 381647520

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Least Common Multiple of 67668 and 67680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67668 and 67680, than apply into the LCM equation.

GCF(67668,67680) = 12
LCM(67668,67680) = ( 67668 × 67680) / 12
LCM(67668,67680) = 4579770240 / 12
LCM(67668,67680) = 381647520

Least Common Multiple (LCM) of 67668 and 67680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67668 and 67680. First we will calculate the prime factors of 67668 and 67680.

Prime Factorization of 67668

Prime factors of 67668 are 2, 3, 5639. Prime factorization of 67668 in exponential form is:

67668 = 22 × 31 × 56391

Prime Factorization of 67680

Prime factors of 67680 are 2, 3, 5, 47. Prime factorization of 67680 in exponential form is:

67680 = 25 × 32 × 51 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 67668 and 67680.

LCM(67668,67680) = 25 × 32 × 56391 × 51 × 471
LCM(67668,67680) = 381647520