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What is the Least Common Multiple of 67821 and 67830?

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 67821 and 67830 is 1533432810.

LCM(67821,67830) = 1533432810

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Least Common Multiple of 67821 and 67830 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67821 and 67830, than apply into the LCM equation.

GCF(67821,67830) = 3
LCM(67821,67830) = ( 67821 × 67830) / 3
LCM(67821,67830) = 4600298430 / 3
LCM(67821,67830) = 1533432810

Least Common Multiple (LCM) of 67821 and 67830 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67821 and 67830. First we will calculate the prime factors of 67821 and 67830.

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

Prime Factorization of 67830

Prime factors of 67830 are 2, 3, 5, 7, 17, 19. Prime factorization of 67830 in exponential form is:

67830 = 21 × 31 × 51 × 71 × 171 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 67821 and 67830.

LCM(67821,67830) = 31 × 131 × 371 × 471 × 21 × 51 × 71 × 171 × 191
LCM(67821,67830) = 1533432810