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What is the Least Common Multiple of 10815 and 10820?

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 10815 and 10820 is 23403660.

LCM(10815,10820) = 23403660

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Least Common Multiple of 10815 and 10820 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10815 and 10820, than apply into the LCM equation.

GCF(10815,10820) = 5
LCM(10815,10820) = ( 10815 × 10820) / 5
LCM(10815,10820) = 117018300 / 5
LCM(10815,10820) = 23403660

Least Common Multiple (LCM) of 10815 and 10820 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10815 and 10820. First we will calculate the prime factors of 10815 and 10820.

Prime Factorization of 10815

Prime factors of 10815 are 3, 5, 7, 103. Prime factorization of 10815 in exponential form is:

10815 = 31 × 51 × 71 × 1031

Prime Factorization of 10820

Prime factors of 10820 are 2, 5, 541. Prime factorization of 10820 in exponential form is:

10820 = 22 × 51 × 5411

Now multiplying the highest exponent prime factors to calculate the LCM of 10815 and 10820.

LCM(10815,10820) = 31 × 51 × 71 × 1031 × 22 × 5411
LCM(10815,10820) = 23403660