Solve Word Problems With Lcm Worksheets [PDF] (6.NS.B.4): 6th ... - Free Printable

Here are the step-by-step solutions for each problem on the worksheet.

Problem 1
* Step 1: Identify the time it takes for each person to complete a lap. Ramesh takes 4 minutes, and Ciara takes 3 minutes.
* Step 2: To find when they meet again at the start, we need the Least Common Multiple (LCM) of 4 and 3.
* Step 3: List the multiples of each number:
* Multiples of 4: 4, 8, 12, 16...
* Multiples of 3: 3, 6, 9, 12, 15...
* Step 4: The smallest number that appears in both lists is 12.

Problem 2
* Step 1: Identify the schedule for each activity. Violin is every 6 days, and swimming is every 2 days.
* Step 2: Find the LCM of 6 and 2.
* Step 3: Since 6 is a multiple of 2 ($2 \times 3 = 6$), the least common multiple is simply 6.
* Multiples of 6: 6, 12...
* Multiples of 2: 2, 4, 6, 8...

Problem 3
* Step 1: Identify the rhythm intervals. The shaker is every 10 seconds, and the drum is every 12 seconds.
* Step 2: Find the LCM of 10 and 12.
* Step 3: List the multiples:
* Multiples of 10: 10, 20, 30, 40, 50, 60, 70...
* Multiples of 12: 12, 24, 36, 48, 60, 72...
* Step 4: The first number they share is 60.

Problem 4
* Step 1: Identify the inspection patterns. Teesta checks every 15th widget, and Eric checks every 12th widget.
* Step 2: Find the LCM of 15 and 12 to see which widget number they both check.
* Step 3: List the multiples:
* Multiples of 15: 15, 30, 45, 60, 75...
* Multiples of 12: 12, 24, 36, 48, 60, 72...
* Step 4: The first matching number is 60.

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Final Answer:
1. 12 minutes
2. 6 days
3. 60 seconds
4. 60