the LCM of 15 and 9 is​

Sagot :

Answer:

Least common multiple (LCM) of 9 and 15 is 45.

Step-by-step explanation:

Least Common Multiple of 9 and 15 with GCF FormulaThe formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b)We need to calculate greatest common factor 9 and 15, than apply into the LCM equation.

[tex] \\ GCF(9,15) = 3

\\ LCM(9,15) = ( 9 × 15) / 3

\\ LCM(9,15) = 135 / 3

\\ LCM(9,15) = 45[/tex]

Least Common Multiple (LCM) of 9 and 15 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 15. First we will calculate the prime factors of 9 and 15.

Prime Factorization of 9

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

[tex]9 = 32[/tex]

Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:

[tex]15 = 31 × 51[/tex]

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 15.

[tex]LCM(9,15) = 32 × 51

\\ LCM(9,15) = 45[/tex]

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