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What is the Least Common Multiple of 1829 and 1840?

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 1829 and 1840 is 3365360.

LCM(1829,1840) = 3365360

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Least Common Multiple of 1829 and 1840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1829 and 1840, than apply into the LCM equation.

GCF(1829,1840) = 1
LCM(1829,1840) = ( 1829 × 1840) / 1
LCM(1829,1840) = 3365360 / 1
LCM(1829,1840) = 3365360

Least Common Multiple (LCM) of 1829 and 1840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1829 and 1840. First we will calculate the prime factors of 1829 and 1840.

Prime Factorization of 1829

Prime factors of 1829 are 31, 59. Prime factorization of 1829 in exponential form is:

1829 = 311 × 591

Prime Factorization of 1840

Prime factors of 1840 are 2, 5, 23. Prime factorization of 1840 in exponential form is:

1840 = 24 × 51 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 1829 and 1840.

LCM(1829,1840) = 311 × 591 × 24 × 51 × 231
LCM(1829,1840) = 3365360