The Least Common Multiple (LCM) by long division method, suitable for Class 5 understanding, involves finding the smallest number that is a multiple of two or more given numbers. Here's how it works:
Steps for LCM by Long Division
Based on the reference information, here are the steps explained simply:
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List the Numbers: Write down the numbers for which you want to find the LCM.
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Divide by the Smallest Prime Number: Start by dividing the numbers by the smallest prime number (2).
- Write the prime number to the left.
- Divide each of the numbers by this prime number.
- If a number is divisible, write the quotient (the result of the division) below it.
- If a number is not divisible, simply bring that number down to the next row.
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Repeat with the Next Smallest Prime Number: Continue dividing the numbers in the next row by the next smallest prime number (3, 5, 7, 11, etc.). Repeat the process of dividing and bringing down numbers that are not divisible.
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Continue Until All are 1: Keep repeating the division process until all the numbers in the last row become 1.
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Multiply the Divisors: Finally, multiply all the prime numbers that you used as divisors on the left side. The product is the LCM.
Example
Let's find the LCM of 12 and 18:
| 2 | 12 | 18 |
|---|---|---|
| 2 | 6 | 9 |
| 3 | 3 | 9 |
| 3 | 1 | 3 |
| 1 | 1 |
Therefore, LCM (12, 18) = 2 x 2 x 3 x 3 = 36
Explanation with Reference Details
- Step 1: We took the numbers 12 and 18. (From reference: "Step 1: Take the provided numbers and divide them by the least prime integer.")
- Step 2: We divided them by the least prime number, 2. 12/2 = 6 and 18/2 = 9. (From reference: "Step 2: In the second row, write the quotient and the number that is not divisible by the previous prime number.")
- Step 3: We continued dividing by prime numbers until all numbers became 1. (From reference: "Step 3: Divide the integers by the next lowest prime number. Step 4: Keep dividing until the remaining is a prime number or one.")
- Final Step: Multiplying all divisors gives us the LCM (36).
Key Points to Remember
- Always start with the smallest prime number (2).
- If a number is not divisible, just bring it down to the next row.
- Continue the process until all numbers become 1.
- The LCM is the product of all the prime divisors.
