Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
This question was previously asked in
SSC CGL Tier 2 Quant Previous Paper 3 [Held On: 18 November 2020]
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- 366
- 634
- 384
- 364
Answer [Detailed Solution Below]
Option 4 : 364
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15 Questions 15 Marks 9 Mins
Concept Used-
The least number which is divisible by several numbers is the LCM of such numbers.
Calculation-
The least number which is divisible by 12, 18, 24 and 30 = LCM of 12, 18, 24 and 30
⇒ 360
Now the least number which leaves remainder as 4 when divided by 12, 18, 24 and 30 = 360 + 4
⇒ 364
Now, 364 is divisible by 7.
∴ 364 is the required number.
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Find the least number which divided by 27, 35, 45 and 49 leaves the remainder 6 in each case?
Solution[By Examveda Team]
ANSWER = 6621
The least number which is divide by 27, 35, 45, 49 is their LCM.
27 = 3 * 3 * 3
35 = 5 * 7
45 = 3 * 3 * 5
49 = 7 * 7
So their LCM = 3 * 3 * 3 * 5 * 7 * 7 = 6615
Now just add 6 to 6615, to get the required number.
Required number = 6615 + 6 = 6621
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Solution
The correct option is C 151
To find the least number which is
divisible by 12, 16 ,24 and 36, we need to find L.C.M. of these numbers.
212,16,24,3626,8,12,1823,4,6,923,2,3,933,1,3,931,1,1,31,1,1,1
L.C.M. of 12, 16, 24, 36 =2×2×2×2×3×3=144
Least Number which when divided by 12, 16 ,24 and 36 leaves a remainder 7 in each case =144+7=151