25 Unique M C Q on H C F and L C M for school competative exams

 

Basic Questions:

1. Find the HCF of 24 and 36.

2. Find the LCM of 15 and 20.

3. The HCF of two numbers is 12, and their LCM is 180. If one number is 36, find the other.

4. Find the HCF of 72, 108, and 144.

5. Find the LCM of 8, 12, and 15.

6. Two numbers have HCF = 6 and LCM = 120. If one number is 30, find the other.

7. The sum of two numbers is 50, and their HCF is 5. What is the possible LCM?

8. Find the LCM of the first five prime numbers.

9. Find the HCF of 120 and 180 using the prime factorization method.

10. The product of two numbers is 540, and their HCF is 6. Find their LCM.

Intermediate-Level Questions:

11. The HCF of 16 and 28 is 4. What is their LCM?

12. The LCM of two co-prime numbers is 117. What is their HCF?

13. The HCF of three numbers is 3, and their LCM is 252. Find the missing number if two of them are 9 and 14.

14. Find the smallest number that is exactly divisible by 9, 12, and 18.

15. The LCM of 72 and 90 is 360. Find their HCF.

16. Three bells ring at intervals of 4, 6, and 8 minutes. After how many minutes will they ring together?

17. If the HCF of two numbers is 18 and their LCM is 540, find the product of the numbers.

18. The LCM of two numbers is 84, and one number is 12. Find the other number if their HCF is 4.

19. A number when divided by 6, 9, and 15 leaves a remainder of 3 in each case. Find the smallest such number.

20. The product of two numbers is 168, and their HCF is 4. Find their LCM.

Advanced-Level Questions:

21. Find the greatest number that will divide 125, 150, and 200 exactly.

22. Find the least number which is exactly divisible by 4, 5, and 6 but leaves a remainder of 3 when divided by 7.

23. A gardener plants 36, 48, and 60 trees in three different rows. Find the maximum number of rows possible if the same number of trees is to be planted in each row.

24. Find the LCM of the fractions 2/3, 3/4, and 5/6.

25. Find the HCF of the fractions 8/9, 12/15, and 16/25.

     

     

    Here are the answers to all 25 questions on HCF and LCM:

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    Basic Questions:

26. HCF of 24 and 36 = 12

27. LCM of 15 and 20 = 60

28. HCF × LCM = Product of numbers → $12 \times 180 = 36 \times x$ → $x = 60$

29. HCF of 72, 108, 144 = 36

30. LCM of 8, 12, and 15 = 120

31. HCF × LCM = Product of numbers → $6 \times 120 = 30 \times x$ → $x = 24$

32. Possible LCMs: Any multiple of (50 ÷ 5) = 10, so possible LCM = 10, 20, 30, etc.

33. LCM of first five prime numbers (2,3,5,7,11) = 2310

34. HCF of 120 and 180 (Prime factorization method): $120 = 2^3 \times 3 \times 5$, $180 = 2^2 \times 3^2 \times 5$ → HCF = $2^2 \times 3 \times 5 = 60$

35. LCM = (Product of numbers) / HCF → $540 / 6 = 90$

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Intermediate-Level Questions:

11. LCM = (Product of numbers) / HCF → $(16 × 28) / 4 = 112$

12. HCF of two co-prime numbers is always 1.

13. HCF × LCM = Product of numbers → $3 \times 252 = 9 \times 14 \times x$ → $x = 6$

14. LCM of 9, 12, 18 = 36

15. HCF of 72 and 90 (Using prime factorization) = 18

16. LCM of 4, 6, and 8 = 24 minutes

17. Product of two numbers = HCF × LCM → $18 \times 540 = 9720$

18. Other number = (LCM × HCF) / Given number → $(84 × 4) / 12 = 28$

19. LCM of 6, 9, and 15 = 90, adding remainder 3 → 93

20. LCM = (Product of numbers) / HCF → $168 / 4 = 42$

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Advanced-Level Questions:

21. HCF of 125, 150, and 200 = 25

22. LCM of 4, 5, and 6 = 60, required number = 60 × k + 3 (Check divisibility by 7) → Smallest number = 123

23. HCF of 36, 48, 60 (to divide into equal rows) = 12 rows

24. LCM of fractions = LCM (Numerators) / HCF (Denominators)

• LCM of 2, 3, 5 = 30

• HCF of 3, 4, 6 = 1

• LCM = 30/1 = 30

25. HCF of fractions = HCF (Numerators) / LCM (Denominators)

• HCF of 8, 12, 16 = 4

• LCM of 9, 15, 25 = 225

• HCF = 4/225

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Now you have all the answers! Let me know if you need explanations for any. 😊🔥