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What is the Least Common Multiple of 30369 and 30380?

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 30369 and 30380 is 922610220.

LCM(30369,30380) = 922610220

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Least Common Multiple of 30369 and 30380 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30369 and 30380, than apply into the LCM equation.

GCF(30369,30380) = 1
LCM(30369,30380) = ( 30369 × 30380) / 1
LCM(30369,30380) = 922610220 / 1
LCM(30369,30380) = 922610220

Least Common Multiple (LCM) of 30369 and 30380 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30369 and 30380. First we will calculate the prime factors of 30369 and 30380.

Prime Factorization of 30369

Prime factors of 30369 are 3, 53, 191. Prime factorization of 30369 in exponential form is:

30369 = 31 × 531 × 1911

Prime Factorization of 30380

Prime factors of 30380 are 2, 5, 7, 31. Prime factorization of 30380 in exponential form is:

30380 = 22 × 51 × 72 × 311

Now multiplying the highest exponent prime factors to calculate the LCM of 30369 and 30380.

LCM(30369,30380) = 31 × 531 × 1911 × 22 × 51 × 72 × 311
LCM(30369,30380) = 922610220