HCF and LCM Problems and Solutions

• 1. Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively

  1. 19
  2. 17
  3. 13
  4. 9

  Answer :

  Option B

  Explanation:

  Answer will be HCF of (400-9, 435-10, 541-14)
  
  HCF of (391, 425, 527) = 17

• 2. The H.C.F. and L.C.M. of two numbers are 12 and 5040 respectively If one of the numbers is 144, find the other number

  1. 400
  2. 256
  3. 120
  4. 420

  Answer :

  Option D

  Explanation:

  Solve this question by using below formula.
  Product of 2 numbers = product of their HCF and LCM
  
  144 * x = 12 * 5040
  
  x = (12*5040)/144 = 420

• 3. The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is

  1. 16cm
  2. 25cm
  3. 15cm
  4. 35cm

  Answer :

  Option D

  Explanation:

  So by now, you must be knowing this is a question of HCF, right.
  H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.

• 4. If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find other

  1. 34
  2. 77
  3. 12
  4. 45

  Answer :

  Option B

  Explanation:

  For any this type of question, remember
  Product of two numbers = Product of their HCF and LCM
  
  So Other number = \begin{aligned} \frac{693 \times 11}{99} \end{aligned} = 77

• 5. Find the HCF of 2.1, 1.05 and 0.63

  1. 0.44
  2. 0.64
  3. 0.21
  4. None of above

  Answer :

  Option C

  Explanation:

  To solve this question quickly, first remove decimal by multiplying each term with 100,
  Then terms become 210, 105, 63
  Then HCF of above terms is 21,
  So Answer is 0.21

• 6. What will be the LCM of 8, 24, 36 and 54

  1. 54
  2. 108
  3. 216
  4. 432

  Answer :

  Option C

  Explanation:

  LCM of 8-24-36-54 will be
  2*2*2*3*3*3 = 216

• 7. Find the LCM of \begin{aligned} \frac{2}{3}, \frac{4}{6}, \frac{8}{27} \end{aligned}

  1. \begin{aligned} \frac{2}{27} \end{aligned}
  2. \begin{aligned} \frac{8}{3} \end{aligned}
  3. \begin{aligned} \frac{2}{3} \end{aligned}
  4. \begin{aligned} \frac{8}{27} \end{aligned}

  Answer :

  Option B

  Explanation:

  Whenever we have to solve this sort of question, remember the formula.
  LCM = \\begin{aligned} \\frac{HCF of Denominators}{LCM of Numerators} \\end{aligned}
  So answers will be option 2,
  Please also give attention to the difference in formula of HCF and LCM