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What is the Least Common Multiple of 67300 and 67305?

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 67300 and 67305 is 905925300.

LCM(67300,67305) = 905925300

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Least Common Multiple of 67300 and 67305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67300 and 67305, than apply into the LCM equation.

GCF(67300,67305) = 5
LCM(67300,67305) = ( 67300 × 67305) / 5
LCM(67300,67305) = 4529626500 / 5
LCM(67300,67305) = 905925300

Least Common Multiple (LCM) of 67300 and 67305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67300 and 67305. First we will calculate the prime factors of 67300 and 67305.

Prime Factorization of 67300

Prime factors of 67300 are 2, 5, 673. Prime factorization of 67300 in exponential form is:

67300 = 22 × 52 × 6731

Prime Factorization of 67305

Prime factors of 67305 are 3, 5, 7, 641. Prime factorization of 67305 in exponential form is:

67305 = 31 × 51 × 71 × 6411

Now multiplying the highest exponent prime factors to calculate the LCM of 67300 and 67305.

LCM(67300,67305) = 22 × 52 × 6731 × 31 × 71 × 6411
LCM(67300,67305) = 905925300