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What is the Least Common Multiple of 67340 and 67344?

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 67340 and 67344 is 1133736240.

LCM(67340,67344) = 1133736240

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Least Common Multiple of 67340 and 67344 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67340 and 67344, than apply into the LCM equation.

GCF(67340,67344) = 4
LCM(67340,67344) = ( 67340 × 67344) / 4
LCM(67340,67344) = 4534944960 / 4
LCM(67340,67344) = 1133736240

Least Common Multiple (LCM) of 67340 and 67344 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67340 and 67344. First we will calculate the prime factors of 67340 and 67344.

Prime Factorization of 67340

Prime factors of 67340 are 2, 5, 7, 13, 37. Prime factorization of 67340 in exponential form is:

67340 = 22 × 51 × 71 × 131 × 371

Prime Factorization of 67344

Prime factors of 67344 are 2, 3, 23, 61. Prime factorization of 67344 in exponential form is:

67344 = 24 × 31 × 231 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 67340 and 67344.

LCM(67340,67344) = 24 × 51 × 71 × 131 × 371 × 31 × 231 × 611
LCM(67340,67344) = 1133736240