LCM of 9, 12, 24, 36, 45, 54 by division method. Please provide a picture.
The Correct Answer and Explanation is:
The least common multiple (LCM) of 9, 12, 24, 36, 45, and 54 by the division method is 1080.
Here is the picture showing the division method step by step:
Explanation
The division method is a systematic way to find the least common multiple (LCM) of a set of numbers. This approach involves dividing the numbers by prime numbers such as 2, 3, 5, and so on, until all resulting numbers are reduced to 1. The LCM is then the product of all prime numbers used in the process.
We begin with the set of numbers: 9, 12, 24, 36, 45, and 54. The smallest prime number is 2. We divide all numbers divisible by 2 and leave the others unchanged. For instance, 12, 24, 36, and 54 are divisible by 2, so they are divided while 9 and 45 remain the same. We continue this process with each resulting row, always dividing by the smallest prime number that can divide at least one number in the row. When no number is divisible by the current prime, we move to the next prime.
Each time we divide, we write the prime number to the left and the new row of numbers to the right. This continues until every number in the row becomes 1. All the prime numbers used in this process are then multiplied together. In this case, the prime numbers used are: 2 (multiple times), 3 (multiple times), and 5.
The final product of all these prime divisors gives us the LCM of the original numbers. So, the LCM of 9, 12, 24, 36, 45, and 54 is calculated to be 1080.
This method ensures that all common and unique prime factors of the numbers are included in the LCM, making it a reliable and visual approach for solving LCM problems.
