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Number System: LCM and HCF Test-1

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Question 1
If the HCF of the two numbers is 23 and the LCM is 298, then which one of the following could one of the numbers be?
A
34
B
43
C
17
D
none
Question 1 Explanation: 
Since the HCF and LCM are given, then HCF must be a factor of LCM, but 23 is not the factor of 298. So, the data is inconsistent and the answer is option D.
Question 2
Let a:b = 4:5 and LCM of a and b is 60, then the smaller number would be:
A
12
B
20
C
16
D
30
Question 2 Explanation: 
We have the number in the ratio of 4 : 5
So let us assume the numbers are 4n and 5n
LCM of these two will be 20n
But LCM  is given i.e. 60
20n = 60
n = 3
So, the smallest number is 12
Question 3
Wordpandit has 1156 boys interns and 1462 girl interns, so he decided to make the groups with each group having the same number of people and without mixing any boys and girls. The maximum size of a group can be:
A
45
B
34
C
102
D
none
Question 3 Explanation: 
Since we are asked for the maximum number of persons in each group,
this number has to be the HCF of both quantities i.e.
HCF of 1156 and 1462. The HCF of these two numbers is 34.
Question 4
Richa , Pranav and Maninder decided to participate in a race. Three of them go round a circular track in 4, 6, 8 hours. They start from the same point at the same time. Find how long will they take to be together at the place again?
A
48
B
24
C
30
D
none
Question 4 Explanation: 
Since they started from the same place,
so the minimum time they will take to get together at the same place is the
LCM of 4, 6 and 8.  So the right answer is option b.
Question 5
Sona wishes to distribute 348 mangoes and 232 oranges equally among a number of beggars, without mixing the oranges and the mangoes (that is a person either gets mangoes or oranges). Find the greatest number of fruits that a beggar can receive?
A
232
B
 212
C
234
D
none
Question 5 Explanation: 
In this case, we need to find the greatest number of fruits that a beggar can receive.
This obviously has to be the HCF of 348 and 232, that is 116.
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