Math question for algebra 1 don't know what to do with lcm

Question

In a computer game adam allows five points for each game he wins, seven points for each game his younger brother wins, and three points for each game the computer wins. After a certain number of games , all three have identical scores. What is the fewest number of games they could have played in order for this tie to be possible? LCM is 105 for 3,5,7

Answer 1

They must have each scored $105$ points (or some multiple, but we want the minimum). How many games must Adam have won to score $105?$ How many games must the computer have won to score $105?$ His brother? Add them up

Answer 2

Adam wins $5*n$ points for $n$ wins

His younger brother wins $7*m$ points for $m$ wins

Computer wins $3*l$ points for $l$ wins

For a tie, $5n=7m=3l= $ some $k$

$k$ is a multiple of $5,7,3$ . We want the minimum $k$ which is nothing but the definition of L.C.M . So, $k=105$

Now, $n=\frac {105}5=21$ and $m=\frac{105}7 = 15$ and $l=\frac {105}3 =35$

Adam won $21$ games, his younger brother won $15$ games and the computer won $35$ games. Total number of games played - $21+15+35=71$