41) The product of two numbers is 1280 and their H.C.F. is 8. The L.C.M. of the number will be ?
Correct Answer - Option
(A)
No Explanation found. Add Explanation and get +2 points.
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42) The HCF of two numbers is 15 and their LCM is 225. If one of the number is 75, then the other number is ?
Correct Answer - Option
(D)
No Explanation found. Add Explanation and get +2 points.
43) The HCF and LCM of two numbers are 12 and 924 respectively. Then the number of such pairs is
Correct Answer - Option
(C)
No Explanation found. Add Explanation and get +2 points.
44) The least number, which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is
Correct Answer - Option
(C)
No Explanation found. Add Explanation and get +2 points.
45) The smallest number, which, when divided by 12 or 10 or 8, leaves remainder 6 in each case, is
Correct Answer - Option
(B)
No Explanation found. Add Explanation and get +2 points.
46) The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder is
Correct Answer - Option
(C)
Explanation :
The LCM of 5, 6, 7 and 8 = 840
∴ Required number = 840 k + 3 which is exactly divisible by 9 for some value of k.
Now, 840 k + 3 = 93 × 9 k + (3k + 3)
When k = 2, 3k + 3 = 9, which is divisible by 9.
∴ Required number = 840 × 2 + 3 = 1683
∴ Required number = 840 k + 3 which is exactly divisible by 9 for some value of k.
Now, 840 k + 3 = 93 × 9 k + (3k + 3)
When k = 2, 3k + 3 = 9, which is divisible by 9.
∴ Required number = 840 × 2 + 3 = 1683
47) The smallest number, which when increased by 5 is divisible by each of 24,32, 36 and 564, is
Correct Answer - Option
(C)
No Explanation found. Add Explanation and get +2 points.
48) The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10 : 15 : 00 AM, then at what time will they again change simultaneously?
Correct Answer - Option
(C)
Explanation :
LCM of 24, 36 and 54 seconds
= 216 seconds
= 3 minutes 36 seconds
= 10 : 18 : 36 a.m.
= 216 seconds
= 3 minutes 36 seconds
= 10 : 18 : 36 a.m.
49) The least number, which when divided by 4, 5 and 6 leaves remainder 1, 2 and 3 respectively, is
Correct Answer - Option
(D)
Explanation :
When a number is divided by P, Q or R leaving remainders X, Y or Z respectively such that the difference between divisor and remainder in each case is same i.e., (P – X) = (Q – Y) = (R – Z) = T (say) then that (least) number must be in the form of (K – T), where K is LCM of P, Q and R
Here 4 – 1 = 3, 5 – 2 = 3, 6 – 3 = 3
∴ The required number = LCM of (4, 5, 6) – 3
= 60 – 3 = 57
Here 4 – 1 = 3, 5 – 2 = 3, 6 – 3 = 3
∴ The required number = LCM of (4, 5, 6) – 3
= 60 – 3 = 57
50) Let the least number of six digits which when divided by 4, 6, 10, 15 leaves in each case same remainder 2 be N. The sum of digits in N is :
Correct Answer - Option
(C)
Explanation :
LCM of 4, 6, 10, 15 = 60
Least number of 6 digits = 100000
The least number of 6 digits which is exactly divisible by 60 = 100000 + (60 – 40) = 100020
∴ Required number (N) = 100020 + 2 = 100022
Hence, the sum of digits = 1 + 0 + 0 + 0 + 2 + 2 = 5
Least number of 6 digits = 100000
The least number of 6 digits which is exactly divisible by 60 = 100000 + (60 – 40) = 100020
∴ Required number (N) = 100020 + 2 = 100022
Hence, the sum of digits = 1 + 0 + 0 + 0 + 2 + 2 = 5
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