SOLUTION: You are asked to arrange the towels in a locker room is stacks of equal size. In stacks of 4, 1 is left over. Stacks of 5, one is left over. The same is true for stacks of 6. You c

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: You are asked to arrange the towels in a locker room is stacks of equal size. In stacks of 4, 1 is left over. Stacks of 5, one is left over. The same is true for stacks of 6. You c      Log On


   

Question 179424: You are asked to arrange the towels in a locker room is stacks of equal size. In stacks of 4, 1 is left over. Stacks of 5, one is left over. The same is true for stacks of 6. You can arrange in stacks of 7 each. What is the smallest possible number of towels.
I did the LCM of 4, 5, and 6 and added one and got 121. Now I don't know how to work the 7 in there. Please help
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
It turns out that the LCM 4, 5, and 6 is actually 60 (since they all go into this value and it is the smallest that all 3 go into)


Now add 1 to 60 to get 61. The question is: does 7 go into 61 (evenly)? The answer is no (since 61%2F7=8.714).


The next smallest number that 4, 5, and 6 go into is just 2 times the LCM 60. So the next value is 60%2A2=120. Now add 1 to 120 to get 121. Now, does 7 go into 121? Once again the answer is no (since 120%2F7=17.143)


So repeat these steps until you find the smallest value that 4, 5, and 6 go into and that 7 goes into the next value



Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the LCM is 60 (not 120)

start with 61, and keep adding 60 until the result is divisible by 7






ANSWER BELOW








301