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What is the Least Common Multiple of 30810 and 30824?

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 30810 and 30824 is 474843720.

LCM(30810,30824) = 474843720

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Least Common Multiple of 30810 and 30824 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30810 and 30824, than apply into the LCM equation.

GCF(30810,30824) = 2
LCM(30810,30824) = ( 30810 × 30824) / 2
LCM(30810,30824) = 949687440 / 2
LCM(30810,30824) = 474843720

Least Common Multiple (LCM) of 30810 and 30824 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30810 and 30824. First we will calculate the prime factors of 30810 and 30824.

Prime Factorization of 30810

Prime factors of 30810 are 2, 3, 5, 13, 79. Prime factorization of 30810 in exponential form is:

30810 = 21 × 31 × 51 × 131 × 791

Prime Factorization of 30824

Prime factors of 30824 are 2, 3853. Prime factorization of 30824 in exponential form is:

30824 = 23 × 38531

Now multiplying the highest exponent prime factors to calculate the LCM of 30810 and 30824.

LCM(30810,30824) = 23 × 31 × 51 × 131 × 791 × 38531
LCM(30810,30824) = 474843720