## Problems on LCM and HCF – Aptitude Questions and Answers

Problems on LCM and HCF aptitude questions and answers section with explanation. Practice online test for various interview, competitive and entrance exams.

1. Find the greatest 4-digit number exactly divisible by 3, 4 and 5?

A.9985 B.9960 C.9957 D.9975

Explanation:

Greatest 4-digit number is 9999. LCM of 3, 4 and 5 is 60. Dividing 9999 with 60, we get remainder 39. Thus, the required number is 9999 – 39 = 9960.

2. Find the lowest 4-digit number which when divided by 3, 4 or 5 leaves a remainder of 2 in each case?

A.1020 B.1026 C.1030 D.1022

Explanation:

Lowest 4-digit number is 1000.
LCM of 3, 4 and 5 is 60.
Dividing 1000 by 60, we get the remainder 40. Thus, the lowest 4-digit number that exactly divisible by 3, 4 and 5 is 1000 + (60 – 40) = 1020.
Now, add the remainder 2 that’s required. Thus, the answer is 1022.

3. Find the greatest number that exactly divides 35, 91 and 840?

A.5          B.6          C.7                D.8

Explanation:

The greatest number that exactly divides 35, 91 and 840 is the HCF of the three numbers. So, calculating HCF we get the answer 7.

4. Find the greatest number which, while dividing 19, 83 and 67, gives a remainder of 3 in each case?

A.16                   B.17          C.18         D.19

Explanation:

Subtract the remainder 3 from each of the given numbers: (19-3)=16, (67-3)=64 and (83-3)=80. Now, find the HCF of the results 16, 64 and 80, we get 16. Thus, the greatest number is 16.

5. Find the greatest number that, while dividing 47, 215 and 365, gives the same remainder in each case?

A.3                   B.4                  C.5                   D.6

Explanation:

Calculate the differences, taking two numbers at a time as follows:
(215-47) = 168
(365-215) = 150
(365-47) = 318
HCF of 168, 150 and 318 we get 6, which is the greatest number, which while dividing 47, 215 and 365 gives the same remainder in each cases is 5.

6. A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width. Find the least number of square tiles of equal size required to cover the entire floor of the room?

A.110          B.124          C.96                   D.117

Explanation:

Length = 6 m 24 cm = 624 cm
Width = 4 m 32 cm = 432 cm
HCF of 624 and 432 = 48
Number of square tiles required = (624 * 432)/(48 * 48) = 13 * 9 = 117

7. A drink vendor has 80 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn’t want to mix any two drinks in a can. What is the least number of cans required?

A.35                   B.37          C.42                   D.30

Explanation:

The number of liters in each can = HCF of 80, 144 and 368 = 16 liters.
Number of cans of Maaza = 80/16 = 5
Number of cans of Pepsi = 144/16 = 9
Number of cans of Sprite = 368/16 = 23
The total number of cans required = 5 + 9 + 23 = 37 cans.

8. The wheels revolve round a common horizontal axis. They make 15, 20 and 48 revolutions in a minute respectively. Starting with a certain point on the circumference down wards. After what interval of time will they come together in the same position?

A.1 min B.2 min C.3 min D.None

Explanation:

Time for one revolution = 60/15 = 4
60/ 20 = 3
60/48 = 5/4
LCM of 4, 3, 5/4
LCM of Numerators/HCF of Denominators = 60/1 = 60

9. A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?

A.7203 B.2403 C.3603 D.4803

Explanation:

LCM of 16, 20, 25, 45 = 3600
1 * 3600 + 3 = 3603   not divisible by 21
2 * 3600 + 3 = 7203   is divisible by 21

10. Three men start together to travel the same way around a circular track of 11 kilometers in circumference. Their speeds are 4, 5 and 8 kilometers per hour respectively. When will they meet at a starting point?

A.11 hours        B.12 hours        C.220 hours D.22 hours

Explanation:

Time for one round = 11/4, 11/5, 11/8
LCM of 11/4, 11/5, 11/8 = 11/1 = 11

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