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What is the Least Common Multiple of 1815 and 1824?

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 1815 and 1824 is 1103520.

LCM(1815,1824) = 1103520

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Least Common Multiple of 1815 and 1824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1815 and 1824, than apply into the LCM equation.

GCF(1815,1824) = 3
LCM(1815,1824) = ( 1815 × 1824) / 3
LCM(1815,1824) = 3310560 / 3
LCM(1815,1824) = 1103520

Least Common Multiple (LCM) of 1815 and 1824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1815 and 1824. First we will calculate the prime factors of 1815 and 1824.

Prime Factorization of 1815

Prime factors of 1815 are 3, 5, 11. Prime factorization of 1815 in exponential form is:

1815 = 31 × 51 × 112

Prime Factorization of 1824

Prime factors of 1824 are 2, 3, 19. Prime factorization of 1824 in exponential form is:

1824 = 25 × 31 × 191

Now multiplying the highest exponent prime factors to calculate the LCM of 1815 and 1824.

LCM(1815,1824) = 31 × 51 × 112 × 25 × 191
LCM(1815,1824) = 1103520