here are 32 forwards and 80 guards in Leo's basketball league.
Leo must include all players on a team and wants each team to have the same number of forwards and the same number of guards.
If Leo creates the greatest number of teams possible, how many guards will be on each team?
16 teams ... 2 forwards and 5 guards each
12
Well, Leo is in quite a pickle! With 32 forwards and 80 guards, he needs to distribute them evenly among teams. So, let's see if we can help him out using a bit of clown logic!
First, we need to find the common number of forwards and guards to make teams as balanced as possible. The greatest common divisor (GCD) between 32 and 80 is 16. So, Leo can create teams of 16 players each.
Since each team needs to have the same number of forwards and guards, we can divide 16 by 2 (half for forwards and half for guards) to find out how many guards will be on each team.
Therefore, each team will have 8 guards. Leave it to Leo to make sure both the forwards and guards have someone to pass the ball to!
To find out how many guards will be on each team, we need to calculate the common number of guards that can be evenly divided among the teams.
The first step is to determine the greatest common divisor (GCD) of the number of guards, which is 80, and the number of forwards, which is 32. The GCD will represent the maximum number of guards that can be evenly divided among all teams.
To calculate the GCD, we can use an algorithm such as Euclid's algorithm. However, in this case, we can easily determine the GCD by observing that 80 is divisible by 16 and 32 is divisible by 8. Therefore, the GCD of 80 and 32 is the smaller value, which is 8.
Now that we know the GCD is 8, we can conclude that each team will have 8 guards. This is because 8 is the largest number of guards that can be evenly divided among all the teams while also satisfying the condition that each team has the same number of guards.
Therefore, each team in Leo's basketball league will have 8 guards.
You are first of all looking for the LCM of 32 and 80
Don't know which algorithm you learned , but here is one of them:
32 = 2*2*2*2*2
80 = 2*2*2*2*5
So you will need 2*2*2*2*2*5 = 160
160/32 = 5 <------ forwards
160/80 = 2 <----- guards
80/5 = 16
32/2 = 16
So they can form 16 teams, with each team having 2 guards and 5 forwards.
Check: all players are used, each team contains the same number and
combination of players.