Answer :
Answer:
Cameron can make
18
identical necklaces, each containing 5 green and 6
Assume, each necklace contains
G
green and
B
blue beads and we have
N
such necklaces. All these variables are natural numbers.
Then we can establish the following equations in natural numbers:
N
⋅
G
=
90
N
⋅
B
=
108
Our task is to find a maximum
N
for which these two equations have a solution in natural numbers.
Obviously,
N
is a maximum common denominator of
90
and
108
.
To find the maximum common denominator of
90
and
108
, let's represent these two numbers as a product of prime numbers:
90
=
2
⋅
3
⋅
3
⋅
5
108
=
2
⋅
2
⋅
3
⋅
3
⋅
3
As we see, the maximum common denominator (a product of all prime numbers that are identical for both
90
and
108
) is
P
=
2
⋅
3
⋅
3
=
18
Therefore, assigning
N
=
18
,
G
=
5
and
B
=
6
, we obtain the solution:
Maximum number of identical necklaces is
N
=
18
with each necklace containing
G
=
5
green beads and
B
=
6