HCF and LCM Problems and Solutions

• 15. Reduce \begin{aligned}
  \frac{368}{575}
  \end{aligned} to the lowest terms.

  1. \begin{aligned} \frac{30}{25} \end{aligned}
  2. \begin{aligned} \frac{28}{29} \end{aligned}
  3. \begin{aligned} \frac{28}{29} \end{aligned}
  4. \begin{aligned} \frac{16}{25} \end{aligned}

  Answer :

  Option D

  Explanation:

  We can do it easily by in two steps
  Step1: We get the HCF of 368 and 575 which is 23
  Step2: Divide both by 23, we will get the answer 16/25

• 16. Find the HCF 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 A

  Explanation:

  Whenever we have to solve this sort of question, remember the formula.
  HCF = \begin{aligned} \frac{HCF of Numerators}{LCM of Denominators} \end{aligned}
  So answers will be option 1

• 17. The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is

  1. 48
  2. 22
  3. 56
  4. 27

  Answer :

  Option A

  Explanation:

  Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.
  So, the numbers 12 and 16.
  L.C.M. of 12 and 16 = 48.

• 18. LCM of two numbers is 7700 and HCF is 11. If one number is 308 then other number is

  1. 269
  2. 285
  3. 300
  4. 275

  Answer :

  Option D

• 19. Find the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectively

  1. 125
  2. 127
  3. 129
  4. 131

  Answer :

  Option B

  Explanation:

  In this type of question, its obvious we need to calculate the HCF, trick is
  HCF of (1661 - 10) and (2045 -13)
  = HCF (1651, 2032) = 127

• 20. Find the largest number which divides 62,132,237 to leave the same reminder

  1. 30
  2. 32
  3. 35
  4. 45

  Answer :

  Option C

  Explanation:

  Trick is HCF of (237-132), (132-62), (237-62)
  = HCF of (70,105,175) = 35

• 21. Find the largest number of four digits which is exactly divisible by 27,18,12,15

  1. 9700
  2. 9710
  3. 9720
  4. 9730

  Answer :

  Option C

  Explanation:

  LCM of 27-18-12-15 is 540.
  After dividing 9999 by 540 we get 279 remainder.
  So answer will be 9999-279 = 9720