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Study the following questions carefully and choose the right answer:
1
The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case, is:
» Explain it
D
Given numbers are: 6, 9, 12, 15, 18
 
LCM of given numbers = 180
 
So, 180 + 2 = 182 is the number that leaves 2 as a remainder.

Hence, option D is correct.
 
2
The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be
» Explain it
A
Let two numbers are 98x and 98y. Then, 
 
Product of number = Product of HCF and LCM
 
98x × 98y = 98 × 2352
 
xy = 24
 
Let x = 8 and y = 3                 (As Co-prime factors of 24 be 8 and 3) 
 
Then, Sum of number = 98 × 8 + 98 × 3 = 98 (11) = 1078

Hence, option A is correct.
 
3
The LCM of two numbers is 2376 while their HCF is 33. If one of the numbers is 297, then the other number is
» Explain it
B
Given,

LCM of two numbers = 2376

HCF of two numbers = 33

One of the number = 297

∵    (HCF of two numbers) × (LCM of two numbers) = (First number) × (Second number)

     Second number =   33 × 2376  = 264
297

Hence, option B is correct.

4
The product of HCF and LCM of 18 and 15 is
» Explain it
D
HCF of 18 and 15 = 3
 
LCM of 18 and 15 = 90
 
∴    Product of HCF and LCM of both numbers = 3 × 90 = 270.

Hence, option D is correct,
 
5
Three planets revolve round the Sun once in 200, 250 and 300 days, respectively in their own orbits. When do they all come relatively to the same position as at a certain point of time in their orbits?
» Explain it
A
Given that, three planets revolves the Sun once in 200, 250 and 300 days, respectively in their own orbits.
 
∴     Required time = LCM of (200, 250 and 300) = 3000 days
 
Hence, after 3000 days they all come relatively to the same position as at a certain point of time in their orbits.

Hence, option A is correct.