LCM and HCF

1

There are five hobby clubs in a college viz., photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days?

  1. 5
  2. 3
  3. 18
  4. 10
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2

Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

  1. 75 m 60 cm
  2. 50 m 40 cm
  3. 25 m 20 cm
  4. 75 m 60 cm
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3

In a fire range, four shooters are firing at their respective targets. The first, the second, the third and the fourth shooter hit the target once in every 5, 6, 7 and 8 seconds respectively. If all of them hit the target at 9:00 am, when will they hit their target together again.

  1. 9:04 am
  2. 9:08 am
  3. 9:10 am
  4. 9:14 am
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4

What is the number of integral solutions of the equations HCF(a,b) = 5 and a + b = 65?

  1. Exactly one
  2. Infinitely many
  3. Less than 65
  4. None
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5

If for integer a, b and c if HCF(a,b) = 1 and HCF(a,c) = 1, then which one of the following is correct?

  1. HCF(a,bc) = a
  2. HCF(a,bc) = b
  3. HCF(a,bc) = 1
  4. None
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6

What is the HCF of 8(x5 - x3 + x) and 28(x6 + 1)?

  1. (x4 + 1 - x2)
  2. 4(x4 + 1 - x2)
  3. 2(x4 + 1 - x2)
  4. None
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7

The product of two numbers is 6912 and their GCD is 24. What is their LCM

  1. 296
  2. 288
  3. 286
  4. 280
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8

What is the LCM of 2/3, 7/9, 14/15?

  1. 14/3
  2. 1/3
  3. 2/3
  4. 7/3
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9

The sum of two positive integers is 52 and their LCM is 168. What is the ratio between the numbers?

  1. 2 : 3
  2. 5 : 4
  3. 7 : 6
  4. 7 : 8
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10

The HCF of two expressions p and q is 1. What is the reciprocal of their LCM?

  1. p + q
  2. p – q
  3. pq
  4. (pq)-1
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11

What is the LCM of x3 + 8, x2 + 5x + 6 and x3 + 4x2 + 4x?

  1. x (x + 2)2 (x + 3) (x2 - 2x + 4)
  2. x (x - 2)2 (x - 3) (x2 + 2x + 4)
  3. (x + 2)2 (x + 3) (x2 - 2x + 4)
  4. (x - 2)2 (x - 3) (x2 - 2x + 4)
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