What is the smallest positive integer, greater than 7, that leaves

Question

What is the smallest positive integer, greater than 7, that leaves a remainder of 7 when divided by 9, 13, or 15 ?

A. 1177
B. 592
C. 202
D. 142
E. 124

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Adit_ · Answer

LCM(9,13,15) = 585

Remainder repeats when added continuously lets say 7/9 rem = 7, similarly 7+9/9 rem = 7 and so on

Therefore simply add 7 to the LCM:

585 + 7 = 592

Answer:  Option B

aditya1818 · Answer

Think of it like this:

The number are leaving a remainder of 7 when divided 9, 13, or 15

so if the number is subtracted by 7 then it will be completely divisible by 9,13 and 15

so (number - 7) is divisible by 9,13 and 15

and so for (number - 7) to be divisible by 9,13 and 15; (number - 7) need to be an LCM of 9, 13, and 15

LCM of 9,13 and 15= 585

(number - 7) = 585

Therefore number= 585+7

Question asks smallest= 592
Option(B)

Dereno · Answer

If the smallest number is not mentioned then 7 could be the answer.

Since, mentioned as numbers greater than 7.

The Least Common Multiple (LCM) of 9,13,15 is 585 , which is completely divisible by all the three for the first time.

So, to get a remainder of 7. We need to add 585+7 =  592.

Option B

Navdeep2000 · Answer

The most efficient way to tackle such questions is to begin by finding the LCM of the given numbers. 
LCM of 9,13, and 15 would be 585

Now, since we know that each of our numbers would be a factor of 585, it would only lead to a quotient, with a remainder of 0 when divided by them.

So, if we just add 7 to the LCM, we know it would leave us with a remainder of 7 when we divide by 9,13 or 15.
Therefore, 585+7 = 592.   Option B

egmat · Answer

If a number N leaves the same remainder R when divided by multiple divisors, then (N - R) must be divisible by ALL those divisors.

So if N leaves remainder  7  when divided by  9 ,  13 , and  15 :
→ N - 7 is divisible by  9 ,  13 , AND  15 
→ N - 7 = LCM(9, 13, 15)

Finding the LCM: 
 9  = 32
 13  = 13
 15  = 3 × 5

LCM = 32 × 5 × 13 =  9  ×  5  ×  13  =  585

Finding N: 
N - 7 =  585 
N = 585 + 7 =  592

Answer: B (592)

General Principle: 
 When a number leaves the SAME remainder when divided by multiple numbers:
Step 1: Subtract the remainder
Step 2: Find LCM of all divisors
Step 3: Add the remainder back

ExpertsGlobal5 · Answer

Video explanation:

https://www.youtube.com/watch?v=WV0MZBukiko

What is the smallest positive integer, greater than 7, that leaves

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