LCM and HCF
LCM and HCF - Important Points
| 11. | The greatest number which on dividing 1658 and 2040 leaves remainders 7 and 8 respectively, is: |
|---|
A. 123
B. 127
C. 131
D. 137
View Answer Discuss Work SpaceAnswer: option b
Explanation:
| 12. | A, B and C start at the same time in the same direction to run around a circular track of length 240 m. A , B and C running at 5 m/s, 6 m/sec and 8 m/sec respectively. If all starting at the same point, then after what time will they again meet at the starting point ? |
|---|
A. 4 mins
B. 4 mins 15 secs
C. 3 mins 45 secs
D. 6 mins
View Answer Discuss Work SpaceAnswer: option a
Explanation:
| 13. | The smallest number which when divided by 4, 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is: |
|---|
A. 1677
B. 1683
C. 1687
D. 1692
View Answer Discuss Work SpaceAnswer: option b
Explanation:
L.C.M. of 4, 5, 6, 7, 8 = 840.
Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
Thus, Required number = (840 x 2 + 3) = 1683.
| 14. | The least number which should be subtracted from 2533 so that it becomes exactly divisible by 3, 4, 5 and 6,is: |
|---|
A. 13
B. 17
C. 3
D. 33
View Answer Discuss Work SpaceAnswer: option a
Explanation:
| 15. | The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs are: |
|---|
A. 1
B. 2
C. 3
D. 4
View Answer Discuss Work SpaceAnswer: option b
Explanation:
Let the two numbers be 13a and 13b respectively.
Then, 13a x 13b = 2028
=>ab = 2028 / (13*13) = 12.
Now, the co-primes with product 12 are (1, 12) and (3, 4).
[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]
So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4). Clearly, there are 2 such pairs.
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