The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. In other words, it is the smallest number that can be divided by both numbers without leaving a remainder.
To find the LCM of 9 and 18, we can use the following steps:
- List the multiples of each number:
- Find the smallest multiple that is common to both lists:
The smallest multiple that is common to both lists is 36. Therefore, the LCM of 9 and 18 is 36.
Another way to find the LCM of 9 and 18 is by using the formula:
LCM(9, 18) = (9 x 18) / GCD(9, 18)
where GCD(9, 18) is the Greatest Common Divisor (GCD) of 9 and 18. Using this formula, we can calculate the LCM as follows:
LCM(9, 18) = (9 x 18) / GCD(9, 18) = 162 / 9 = 18
Note that GCD(9,18) = 9
Using prime factorization method
- Factorize the numbers into their prime factors 9 = 3^2 18 = 2*3^2
- Take the highest power of each prime factor 3^2
- Multiply all the prime factors together, it will give the LCM LCM(9, 18) = 3^2*2 = 36
In conclusion, LCM of 9 and 18 is 36. It can be calculated using different methods like listing multiples, using formula and prime factorization method.