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What is the Least Common Multiple of 30495 and 30500?

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 30495 and 30500 is 186019500.

LCM(30495,30500) = 186019500

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Least Common Multiple of 30495 and 30500 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30495 and 30500, than apply into the LCM equation.

GCF(30495,30500) = 5
LCM(30495,30500) = ( 30495 × 30500) / 5
LCM(30495,30500) = 930097500 / 5
LCM(30495,30500) = 186019500

Least Common Multiple (LCM) of 30495 and 30500 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30495 and 30500. First we will calculate the prime factors of 30495 and 30500.

Prime Factorization of 30495

Prime factors of 30495 are 3, 5, 19, 107. Prime factorization of 30495 in exponential form is:

30495 = 31 × 51 × 191 × 1071

Prime Factorization of 30500

Prime factors of 30500 are 2, 5, 61. Prime factorization of 30500 in exponential form is:

30500 = 22 × 53 × 611

Now multiplying the highest exponent prime factors to calculate the LCM of 30495 and 30500.

LCM(30495,30500) = 31 × 53 × 191 × 1071 × 22 × 611
LCM(30495,30500) = 186019500