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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