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What is the Least Common Multiple of 30094 and 30100?

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 30094 and 30100 is 452914700.

LCM(30094,30100) = 452914700

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Least Common Multiple of 30094 and 30100 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30094 and 30100, than apply into the LCM equation.

GCF(30094,30100) = 2
LCM(30094,30100) = ( 30094 × 30100) / 2
LCM(30094,30100) = 905829400 / 2
LCM(30094,30100) = 452914700

Least Common Multiple (LCM) of 30094 and 30100 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30094 and 30100. First we will calculate the prime factors of 30094 and 30100.

Prime Factorization of 30094

Prime factors of 30094 are 2, 41, 367. Prime factorization of 30094 in exponential form is:

30094 = 21 × 411 × 3671

Prime Factorization of 30100

Prime factors of 30100 are 2, 5, 7, 43. Prime factorization of 30100 in exponential form is:

30100 = 22 × 52 × 71 × 431

Now multiplying the highest exponent prime factors to calculate the LCM of 30094 and 30100.

LCM(30094,30100) = 22 × 411 × 3671 × 52 × 71 × 431
LCM(30094,30100) = 452914700