The LCM (Least Common Multiple) by division method for Class 5 involves finding the smallest number that is a multiple of two or more given numbers by repeatedly dividing them by common prime factors.
Understanding the LCM by Division Method
The division method is a straightforward way to calculate the LCM, especially helpful when dealing with multiple numbers. It relies on systematically dividing the numbers by prime numbers until you are left with either prime numbers or 1.
Steps for Finding LCM by Division Method:
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Arrange the Numbers: Write the numbers you want to find the LCM of in a horizontal row, separated by commas.
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Divide by a Common Prime Number: Find a prime number that divides at least two of the numbers. Write this prime number to the left of the numbers.
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Write the Quotients: Divide each number by the prime number. If a number is not divisible, simply bring it down to the next row.
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Repeat: Continue this process with the quotients, always choosing a prime number that divides at least two of the numbers in the row.
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Continue until Prime/1: Keep repeating until all the numbers in the last row are either 1 or prime numbers.
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Multiply the Divisors and Remainders: The LCM is the product of all the prime numbers (divisors) and any remaining prime numbers or 1s in the last row.
Example: Find the LCM of 12, 15, and 20
Here's how to find the LCM of 12, 15, and 20 using the division method:
| Prime Factor | 12 | 15 | 20 |
|---|---|---|---|
| 2 | 6 | 15 | 10 |
| 2 | 3 | 15 | 5 |
| 3 | 1 | 5 | 5 |
| 5 | 1 | 1 | 1 |
LCM = 2 x 2 x 3 x 5 = 60
Therefore, the LCM of 12, 15, and 20 is 60.
Key Points for Class 5 Students
- Prime Numbers: Make sure you're dividing by prime numbers (2, 3, 5, 7, 11, etc.).
- Divisibility Rules: Knowing divisibility rules can help you quickly find common prime factors.
- Practice: The more you practice, the easier it will become!
- Understanding: Emphasize understanding why the method works, not just memorizing steps. The method works because it systematically breaks down each number into its prime factors, ensuring the LCM includes all necessary prime factors with the highest powers present in any of the original numbers.
