28 August, 22:52

# Jenny is making bracelets using different coloredbeads. Jenny has 60 green beads and 105 bluebeads. What is the greatest number of identicalbracelets Jenny can make if she wants to use all ofthe beads?

+1
1. 28 August, 23:10
0

18

identical necklaces, each containing 5 green and 6 blue beads.

Explanation:

Assume, each necklace contains

G

green and

B

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