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HSBC LCM and HCF Questions and Answers Quiz-1

Question 1

Time: 00:00:00

What is the greatest number which divides 639, 1065 and 1491 exactly?

193

183

223

213

233

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Sol : Option 4
H.C.F. of 639 and 1065 is 213. H.C.F. of 213 and 1491 is 213.

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Question 2

Time: 00:00:00

The HCF of two numbers is 29 & their sum is 174. The possible numbers are

1,174

74100

29, 154

29, 145

None of these

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Sol : Option 4
Let the numbers be 29a and 29b. Then, 29a + 29b= 174 or 29(a + b) = 174 or, a + b = 174/29 = 6. Values of co-primes (with sum 6) is(1, 5).
So, the possible pairs of numbers is (29 x 1, 29 x 5) i.e. 29 and 145, which will become the answer.

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Question 3

Time: 00:00:00

Find the side of the largest square slab which can be paved on the floor of a room 5 meters 44cm long and 3 meters 74 cm broad.

56 cm

42 cm

38 cm

48 cm

34 cm

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Sol : Option 4
The side of the square slab is the H.C.F. of 544 and 374 cm i.e. 34.

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Question 4

Time: 00:00:00

The product of two numbers is 6760 and their H.C.F. is 13. How many such pairs can be formed?

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Sol : Option 5
Let the numbers be 13x and 13y. So, 13X ×13 Y = 6760 X×Y=40.
Possible values of (x, y) are (1, 40); (2, 20); (4, 10); (5, 8) Only two acceptable values are (1, 40) and (5, 8).

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Question 5

Time: 00:00:00

The least perfect square number which is divisible by 3, 4, 5, 6 and 8 is

900

1200

2500

3600

1600

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Sol : Option 4
L.C.M. of 3, 4, 5, 6, 8 = 120 ; Required number =2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 = 3600.

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Question 6

Time: 00:00:00

3 different pieces of iron are of varying length are given to a student which are 44cm, 22 cm,55 cm respectively.He has to form rods of maximum length such that no iron waste is left.Find the maximum length of such rod.

28 cm

14 cm

42 cm

63 cm

11 cm

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Sol : Option 5
Maximum possible length of such rod = (H.C.F. of 44, 22, 55)c m = 11cm.

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Question 7

Time: 00:00:00

Find the greatest number which will divide 25, 73 and 97 as so to leave the same remainder in each case?

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Question 8

Time: 00:00:00

Find the greatest number which is such that when 697, 909 and 1227 are divided by it, the remainders are all the same?

112

108

106

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Question 9

Time: 00:00:00

A merchant has three different types of milk: 435 liters, 493 liters and 551 liters. Find the least number of casks of equal size required to store all the milk without mixing.

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Explanation:

HCF of 435, 493, 551 = 29

(453/29) + (493/29) + (551/29) = 51

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Question 10

Time: 00:00:00

A wholesale tea dealer 408 kilograms, 468 kilograms and 516 kilograms of three different qualities of tea. He wants it all to be packed into boxes of equal size without mixing. Find the capacity of the largest possible box?

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Explanation:

HCF of 408, 468, 516 = 12

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