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Test: HCF and LCM- 2 - Mechanical Engineering MCQ

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20 Questions MCQ Test General Aptitude for GATE - Test: HCF and LCM- 2

Test: HCF and LCM- 2 for Mechanical Engineering 2024 is part of General Aptitude for GATE preparation. The Test: HCF and LCM- 2 questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: HCF and LCM- 2 MCQs are made for Mechanical Engineering 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: HCF and LCM- 2 below.

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Test: HCF and LCM- 2 - Question 1

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A rectangular courtyard 140cm long 525cm wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?

A.
64cm
B.
35cm
C.
21cm
D.
28cm
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 1

30 cm = 4 × 5 × 7
525 cm = 5 × 5 × 3 × 7
Hence common factors are 5 and 7
Hence LCM = 5 × 7 = 35

Test: HCF and LCM- 2 - Question 2

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Two containers contain 50 and 125 litres of water respectively. Find the maximum capacity of a container which can measure the water in each container an exact number of times(in litres)

A.
25
B.
11
C.
12
D.
15
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 2

HCF of 50 and 125 = 25

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Test: HCF and LCM- 2 - Question 3

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Two baskets contain 183 and 242 Apples respectively, which are distributed in equal number among children. Find the largest number of apples that can be given, so that 3 apples are left over from the first basket and 2 from the second.

A.
45
B.
40
C.
60
D.
56
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 3

183-3 = 180
142-2 = 240
HCF of 240, 180 = 60

Test: HCF and LCM- 2 - Question 4

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A person has 3 bars whose length are 12,16,24m respectively. He want to cuts the longest possible pieces, all of the same length from each of the 3 bars, what is the length of the each piece, if he is cut without any wastage

A.
12m
B.
20m
C.
6m
D.
4m
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 4

HCF of 12, 16, 24 = 4m

Test: HCF and LCM- 2 - Question 5

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Four bells commence tolling together and toll at the intervals of 3,9,12,15 seconds resp. In 60 minutes how many times they will toll together.

A.
20
B.
21
C.
24
D.
30
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 5

LCM of 3, 9, 12, 15 = 180s = 3m
In 60m = 60/3 = 20⇒ 20+1 = 21

Test: HCF and LCM- 2 - Question 6

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In a seminar the number of participants in Technology, Economics and Science are 150, 90 and 180 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated and all of them being in the same subject.

A.
27
B.
32
C.
30
D.
14
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 6

HCF of 150, 90 and 180 = 30
No of participants can be seated in each room = 30

There are total 420 participants.

As the HCF is 30 i.e. mininum number of participants in each room.

so total rooms required will be 420/30 = 14

Test: HCF and LCM- 2 - Question 7

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Naren, Suraj and Praveen start running around a circular stadium and complete one round in 12s, 9s and 15s respectively. In how much time will they meet again at the starting point ?

A.
2m
B.
2.30m
C.
3m
D.
3.30m
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 7

LCM of 12, 9, 15 =180s = 3m

Test: HCF and LCM- 2 - Question 8

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Three boxes of lengths 60m,30m and 45m are to be cut into pieces of equal length. What is the greatest possible length of each pieces ?

A.
15m
B.
18m
C.
5m
D.
3m
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 8

HCF of 60, 30 and 45m = 15m

Test: HCF and LCM- 2 - Question 9

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In a college, all the students can stand in a row, so that each row has 9, 7 and 12 students. Find the least no of students in the school ?

A.
145
B.
265
C.
186
D.
252
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 9

LCM of 9, 7 and 12 = 252

Test: HCF and LCM- 2 - Question 10

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The HCF of 3 different no is 17, Which of the following cannot be their LCM ?

A.
540
B.
289
C.
340
D.
425
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 10

To check whether the given number is it's LCM or not just divide the LCM by HCF .

1) 540 ÷ 17 = 31.76

2) 289 ÷ 17 = 17

3) 340 ÷ 17 = 20

4) 425 ÷ 17 = 25 .

540 is not divisible by 17.

Hence : 540 is not the LCM .

Test: HCF and LCM- 2 - Question 11

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If the product of two numbers is 2496 and HCF is 8,then the ratio of HCF and LCM is

A.
1:32
B.
39:1
C.
1:39
D.
4:63
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 11

HCF = 8
LCM = Product/HCF Product of the 2 number = 2496
HCF:LCM = 8 : (2496/8) ⇒ 8 : 312 ⇒ 1: 39

Test: HCF and LCM- 2 - Question 12

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The greatest possible length which can be used to measure exactly the lengths 1m 92cm,3m 84cm ,23m 4cm

A.
23
B.
32
C.
36
D.
34
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 12

192 = 4²×2²×3
384 = 4²×2²×6
2304 = 4²×2×6²
HCF = 4²×2 = 16×2 = 32

Test: HCF and LCM- 2 - Question 13

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HCF of 4/3, 8/6, 36/63 and 20/42

A.
4/126
B.
4/8
C.
4/36
D.
4/42
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 13

HCF of numerator(4,8,36,20) = 4
LCM of denominator(3,6,63,42) = 126

Test: HCF and LCM- 2 - Question 14

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Find the LCM of 3/8, 9/32, 33/48, 18/72

A.
3/8
B.
8/33
C.
198/8
D.
8/3
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 14

LCM of numerator(3,9,33,18) = 198
HCF of denominator(8,32,48,72) = 8

Test: HCF and LCM- 2 - Question 15

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The HCF of 2511 and 3402 is

A.
31
B.
42
C.
76
D.
81
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 15

2511 = 81×31
3402 = 81×42
Hence HCF is 81

Test: HCF and LCM- 2 - Question 16

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A gardener had a number of shrubs to plant in rows. At first he tried to plant 8,then 12 and then 16 in a row but he had always 3 shrubs left with him. On trying 7 he had none left. Find the total number of shrubs.

A.
154
B.
147
C.
137
D.
150
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 16

Test: HCF and LCM- 2 - Question 17

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If m and n are two whole numbers and if mⁿ= 49. Find n^m, given that n ≠ 1

A.
118
B.
94
C.
561
D.
128
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 17

49 = 7² = mⁿ
n^m = 2⁷ = 128

Test: HCF and LCM- 2 - Question 18

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What will be the least number which when doubled will be exactly divisible by 12,18,21 and 30?

A.
630
B.
360
C.
603
D.
306
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 18

LCM of 12,18,21 and 30 = 1260
Doubled (divide by 2) = 1260/2 = 630

Test: HCF and LCM- 2 - Question 19

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HCF and LCM of two numbers are 11 and 385 .If one number lies between 75 and 125 then that number is

A.
123
B.
73
C.
77
D.
154
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 19

Product of the two number = 11a×11b = 4235
11a×11ab = 4235/121 = 35
35 = 7 × 5 (co prime)
77 × 11 = 77

Test: HCF and LCM- 2 - Question 20

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If the L.C.M of x and y is z, their H.C.F is

A.
xy/z
B.
xyz
C.
(x + y)/z
D.
z/xy
E.
None of these

Detailed Solution for Test: HCF and LCM- 2 - Question 20

HCF = Product of the 2 number/LCM = XY/Z

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