Target Practice (TP) - LCM and HCF
Total: 10 Questions × 2 Marks = 20 Marks
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Q1. Find the HCF of 24 and 36.
2 Marks
Key: HCF = 12. Factors common to 24 and 36 are 1, 2, 3, 4, 6, 12. Greatest = 12.
Q2. Find the LCM of 8 and 12.
2 Marks
Key: LCM = 24. Multiples of 8: 8, 16, 24... Multiples of 12: 12, 24... First common multiple is 24.
Q3. Find the HCF of 18, 27 and 45.
2 Marks
Key: HCF = 9. 18 = 2 × 3², 27 = 3³, 45 = 5 × 3². Common factor with smallest power is 3² = 9.
Q4. Find the LCM of 15 and 20 using prime factors.
2 Marks
Key: LCM = 60. 15 = 3 × 5, 20 = 2² × 5. LCM = 2² × 3 × 5 = 60.
Q5. Find the least number that is divisible by both 6 and 14.
2 Marks
Key: This is LCM. 6 = 2 × 3, 14 = 2 × 7. LCM = 2 × 3 × 7 = 42.
Q6. What is the greatest number that divides 48 and 72 exactly?
2 Marks
Key: This is HCF. HCF of 48 and 72 = 24.
Q7. Two bells ring at intervals of 12 minutes and 18 minutes. If they ring together now, after how many minutes will they ring together again?
2 Marks
Key: Use LCM. 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 36. They ring together again after 36 minutes.
Q8. Three ropes of lengths 24 m, 36 m and 60 m are to be cut into equal pieces of maximum length. Find the length of each piece.
2 Marks
Key: Use HCF because maximum equal length is asked. HCF of 24, 36, 60 = 12 m.
Q9. If the HCF of two numbers is 6 and their product is 540, and one number is 18, find the other number using LCM × HCF = Product.
2 Marks
Key: Other number = 540 ÷ 18 = 30. So the other number is 30.
Q10. Find both the HCF and LCM of 16 and 24.
2 Marks
Key: 16 = 2⁴, 24 = 2³ × 3. HCF = 2³ = 8. LCM = 2⁴ × 3 = 48.
Self Evaluation
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