Answer: 29 seashells.
Step-by-step explanation:
Suppose that she found N seashells.
When she divides the N seashells by 6, 8 and 12, there is a remainder of 5 seashells.
First, we know that 6 is a multiple of 12, now, for an integer number k:
k*12 is a multiple of 12.
Then:
(k*12 + 5) will have a remaining of 5 when divided for 12 or 6.
The same happens for a number like:
(n*8 + 5) when divided by 8 (where we assumed that n is an integer)
Then we need to find a number that can be written as:
k*12 and n*8
This means that we need to find a common multiple of 12 and 8.
And because we want to find the smaller number of seashells that she could collect, we need to find the smaller common multiple between 12 and 8.
Remember that the smallest common multiple between a and b is:
SCM(a, b) = a*b/(LCM(a,b)
LCM(a,b) = largest common factor between a and b.
We can write:
8 = 2*4
12 = 3*4
So the largest common factor between a and b is 4.
SCM(8,12) = 8*12/4 = 2*12 = 24
and remember that she collected 5 more than this, then:
N = 24 + 5 = 29
if we divide 29 by 8, there is a remainder of 5.
if we divide 29 by 6, there is a remainder of 5.
if we divide 29 by 12, there is a remainder of 5.
