LCM & HCF Work Sheet – 1

Worksheet: LCM and HCF

Class: 6 & 7
Total Marks: 50
Time Allowed: 1 Hour

Part A: Basics of LCM and HCF (15 Marks)

1. Find the Least Common Multiple (LCM) of the following pairs of numbers: (6 Marks)
   a. 4 and 6
   b. 12 and 15
   c. 8 and 10

2. Find the Highest Common Factor (HCF) of the following pairs of numbers: (6 Marks)
   a. 18 and 24
   b. 40 and 60
   c. 14 and 35

3. Write down two pairs of numbers that have: (3 Marks)
   a. LCM = 24
   b. HCF = 6

Part B: Word Problems (20 Marks)

4. Two bells ring at intervals of 4 minutes and 6 minutes. If both bells ring together at 8:00 AM, at what time will they ring together again? (4 Marks)

5. The lengths of two ropes are 120 cm and 150 cm. Find the longest length of rope that can be used to measure both ropes exactly. (4 Marks)

6. Three tankers contain 500 liters, 650 liters, and 800 liters of oil. Find the capacity of the largest container that can be used to empty all three tankers completely. (4 Marks)

7. Two cyclists start from the same point and travel in opposite directions around a circular track of 360 meters. One completes a lap in 90 seconds, and the other in 120 seconds. After how many seconds will they meet at the starting point? (4 Marks)

8. A farmer has three pieces of land measuring 48 m, 60 m, and 72 m. He wants to divide them into equal sections of the largest possible size. What will be the size of each section? (4 Marks)

Part C: Mixed Problems (15 Marks)

9. Fill in the blanks: (5 Marks)
   a. The LCM of 6 and 8 is ___ and their HCF is ___.
   b. The LCM of 9 and 12 is ___ and their HCF is ___.
   c. The LCM of 15 and 20 is ___ and their HCF is ___.

10. Solve: (5 Marks)
    a. Find the smallest number divisible by both 12 and 18.
    b. Find the greatest number that divides both 28 and 36.

11. A school has two buses that arrive every 20 minutes and 30 minutes, respectively. If both buses arrive together at 7:00 AM, when will they arrive together again? (5 Marks)

Part D: Challenge Question (Bonus – 5 Marks)

12. The HCF of two numbers is 16, and their LCM is 240. If one of the numbers is 48, find the other number.

End of Worksheet

Answer Key: LCM and HCF Worksheet

Part A: Basics of LCM and HCF

1. Find the Least Common Multiple (LCM):
   a. LCM of 4 and 6 = 12
   b. LCM of 12 and 15 = 60
   c. LCM of 8 and 10 = 40

2. Find the Highest Common Factor (HCF):
   a. HCF of 18 and 24 = 6
   b. HCF of 40 and 60 = 20
   c. HCF of 14 and 35 = 7

3. Write two pairs of numbers:
   a. LCM = 24: 8 and 6, 12 and 4
   b. HCF = 6: 12 and 18, 30 and 24

Part B: Word Problems

4. Two bells ring together: 8:12 AM

5. Longest length of rope: 30 cm

6. Largest container capacity: 50 liters

7. Time when cyclists meet: 360 seconds (6 minutes)

8. Size of each section: 12 meters

Part C: Mixed Problems

9. Fill in the blanks:
   a. LCM of 6 and 8 = 24, HCF = 2
   b. LCM of 9 and 12 = 36, HCF = 3
   c. LCM of 15 and 20 = 60, HCF = 5

10. Solve:
    a. Smallest number divisible by 12 and 18 = 36
    b. Greatest number that divides 28 and 36 = 4

11. When buses arrive together: 7:30 AM

Part D: Challenge Question (Bonus)

12. The other number: 80

End of Answer Key