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Number System: LCM and HCF Test-2

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Question 1
The product of two numbers is 15300. What could be the maximum value of their H.C.F.?
A
45
B
34
C
30
D
42
Question 1 Explanation: 
Let the two numbers are x and y, and let the HCF of two numbers be f
So the numbers can be written in the form of fx and fy
Now we have the product of two numbers i.e 15300
So we can say that l.c.m. of fx and fy is 15300
So now 15300 = 223252171
And fx * fy = f2xy
So the maximum value of f2 = 223252
And the maximum value of f = 2x3x5 =30
Question 2
What will be the LCM of 3/5, 5/15, 4/5, 7/25?
A
90
B
84
C
45
D
30
Question 2 Explanation: 
Since we know the LCM of fraction is given by
(LCM of numerator) / (HCF of the denominator)
So we have the LCM OF 3,5,4,7 = 420
HCF of  5 ,15 ,5, 25= 5
So the LCM of whole fraction is 420/5=84
Question 3
Let there are three numbers which are in the ratio of 2:3:4 and the value of their LCM is 948 so what is the smallest of three numbers?
A
167
B
168
C
138
D
none
Question 3 Explanation: 
Since we have the ratio of three numbers therefore the
three numbers can be written in the form of 2x, 3x, 4x
We have the LCM of the three numbers i.e.948
So  LCM  of three numbers 2x,3x,4x = 12x where x  is a multiple
So 12x = 948
X = 79
Therefore the smallest number among three is  158, so d is the right answer
Question 4
A number is divided by 5,6,7,8 leaves the remainder 4,5,6,7. Which is the smallest such number?
A
845
B
678
C
989
D
none
Question 4 Explanation: 
The right answer is 839
Since the difference between devisor and the remainder are same so we can say that the number must be the
{(LCM of 5, 6, 7, 8,) – 1} [ 1 is the difference ]
So {lcm of 5,6,7,8}= 840 and the right number is 839
Question 5
Richa can do a work in 6 days and Meera can do the same work in 8 days. So how many days they will take if they work together?
A
24/7
B
23/7
C
49
D
48
Question 5 Explanation: 
Let us assume the total work is ( lcm of 6 and 8 =24)
Now Richa can do 24 units of work in 6 days that means 4 units per day
Meera can do the same work in  8 days that means 3 units per day
Now they both doing the work that means they are dong 7 units per day
So the total time from which they will do the work is 24/7 days i.e  option a
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