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What is the Least Common Multiple of 30800 and 30810?

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 30800 and 30810 is 94894800.

LCM(30800,30810) = 94894800

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Least Common Multiple of 30800 and 30810 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30800 and 30810, than apply into the LCM equation.

GCF(30800,30810) = 10
LCM(30800,30810) = ( 30800 × 30810) / 10
LCM(30800,30810) = 948948000 / 10
LCM(30800,30810) = 94894800

Least Common Multiple (LCM) of 30800 and 30810 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30800 and 30810. First we will calculate the prime factors of 30800 and 30810.

Prime Factorization of 30800

Prime factors of 30800 are 2, 5, 7, 11. Prime factorization of 30800 in exponential form is:

30800 = 24 × 52 × 71 × 111

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

Now multiplying the highest exponent prime factors to calculate the LCM of 30800 and 30810.

LCM(30800,30810) = 24 × 52 × 71 × 111 × 31 × 131 × 791
LCM(30800,30810) = 94894800