To find the Least Common Multiple (LCM) of two numbers, we follow these steps:
1. Identify the numbers: In this case, the numbers are 15 and 9.
2. Find the Greatest Common Divisor (GCD) of the two numbers:
- The GCD is the largest positive integer that divides both numbers without leaving a remainder.
- By evaluating the factors of both numbers:
- Factors of 15: 1, 3, 5, 15
- Factors of 9: 1, 3, 9
- The GCD of 15 and 9 is 3, which is the highest common factor they share.
3. Calculate the LCM using the relationship between the GCD and LCM:
- The formula to find the LCM using the GCD is:
[tex]\[
\text{LCM}(a, b) = \frac{|a \cdot b|}{\text{GCD}(a, b)}
\][/tex]
- Substitute the values:
- [tex]\( a = 15 \)[/tex]
- [tex]\( b = 9 \)[/tex]
- [tex]\( \text{GCD}(15, 9) = 3 \)[/tex]
- Therefore:
[tex]\[
\text{LCM}(15, 9) = \frac{|15 \cdot 9|}{3}
\][/tex]
4. Perform the calculations:
- First, multiply the two numbers:
[tex]\[
15 \cdot 9 = 135
\][/tex]
- Then, divide by their GCD:
[tex]\[
\frac{135}{3} = 45
\][/tex]
Therefore, the Least Common Multiple (LCM) of 15 and 9 is 45.
