LCM and HCF

 

🔹 Basic Concept Questions

  1. Find the HCF of 24 and 36.
  2. Find the LCM of 15 and 20.
  3. Find the HCF of 18, 27, and 45.
  4. Find the LCM of 12, 18, and 30.
  5. Find both HCF and LCM of 8 and 32.

🔹 Using Prime Factorization

  1. Find the HCF of 96 and 144 using prime factorization.
  2. Find the LCM of 72 and 120 using prime factorization.
  3. Find the HCF and LCM of 45 and 75.
  4. Find the HCF of 84, 126, and 210.
  5. Find the LCM of 16, 24, and 40.

🔹 Relation Between HCF and LCM

👉 (Use: Product of numbers = HCF × LCM)

  1. If HCF of two numbers is 6 and their LCM is 180, find the product of the two numbers.
  2. Two numbers have HCF 8 and LCM 160. If one number is 32, find the other.
  3. The product of two numbers is 540 and their HCF is 6. Find their LCM.
  4. If LCM of two numbers is 120 and one number is 24 and HCF is 6, find the other number.
  5. Verify the relation between HCF and LCM for the numbers 18 and 24.

🔹 Word Problems / Application

  1. Find the greatest number that divides 245 and 1029 leaving remainder 5 in each case.
  2. Find the least number which when divided by 12, 15, and 20 leaves remainder 3 in each case.
  3. Three bells ring at intervals of 10, 15, and 20 minutes. If they ring together now, after how many minutes will they ring together again?
  4. Find the greatest number that divides 306 and 657 exactly.
  5. Find the smallest number which is exactly divisible by 8, 12, and 15.