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What is the Least Common Multiple of 67815 and 67821?

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 67815 and 67821 is 1533093705.

LCM(67815,67821) = 1533093705

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Least Common Multiple of 67815 and 67821 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67815 and 67821, than apply into the LCM equation.

GCF(67815,67821) = 3
LCM(67815,67821) = ( 67815 × 67821) / 3
LCM(67815,67821) = 4599281115 / 3
LCM(67815,67821) = 1533093705

Least Common Multiple (LCM) of 67815 and 67821 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67815 and 67821. First we will calculate the prime factors of 67815 and 67821.

Prime Factorization of 67815

Prime factors of 67815 are 3, 5, 11, 137. Prime factorization of 67815 in exponential form is:

67815 = 32 × 51 × 111 × 1371

Prime Factorization of 67821

Prime factors of 67821 are 3, 13, 37, 47. Prime factorization of 67821 in exponential form is:

67821 = 31 × 131 × 371 × 471

Now multiplying the highest exponent prime factors to calculate the LCM of 67815 and 67821.

LCM(67815,67821) = 32 × 51 × 111 × 1371 × 131 × 371 × 471
LCM(67815,67821) = 1533093705