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What is the Least Common Multiple of 30760 and 30765?

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 30760 and 30765 is 189266280.

LCM(30760,30765) = 189266280

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Least Common Multiple of 30760 and 30765 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30760 and 30765, than apply into the LCM equation.

GCF(30760,30765) = 5
LCM(30760,30765) = ( 30760 × 30765) / 5
LCM(30760,30765) = 946331400 / 5
LCM(30760,30765) = 189266280

Least Common Multiple (LCM) of 30760 and 30765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30760 and 30765. First we will calculate the prime factors of 30760 and 30765.

Prime Factorization of 30760

Prime factors of 30760 are 2, 5, 769. Prime factorization of 30760 in exponential form is:

30760 = 23 × 51 × 7691

Prime Factorization of 30765

Prime factors of 30765 are 3, 5, 7, 293. Prime factorization of 30765 in exponential form is:

30765 = 31 × 51 × 71 × 2931

Now multiplying the highest exponent prime factors to calculate the LCM of 30760 and 30765.

LCM(30760,30765) = 23 × 51 × 7691 × 31 × 71 × 2931
LCM(30760,30765) = 189266280