Find the LCM for the given numbers by an appropriate method. 24, 54, and 27 Show your method.
The factors of 24 are 2,2,2,3
the factors of 27 are 3,3,3
The factors of 54 are 3,3,3,3,2
The LCM has to be 2,2,2,3,3,3,3 factors or 8*81
One way to do this is to find the multiples of 54. When you find the number that is also divisible by 24 and 27.
54, 108, 162, 216, 270 . . .
Which of those numbers is also divisible by both 24 and 27?
To find the LCM (Least Common Multiple) of the given numbers (24, 54, and 27), we can follow these steps:
Step 1: Prime factorize each number.
- 24 = 2^3 * 3^1
- 54 = 2^1 * 3^3
- 27 = 3^3
Step 2: Identify the highest power of each prime factor.
- The highest power of 2 is 2^3 = 8.
- The highest power of 3 is 3^3 = 27.
Step 3: Multiply the highest powers of the prime factors together to find the LCM.
- LCM = 8 * 27
- LCM = 216
Therefore, the LCM of 24, 54, and 27 is 216.