Manny makes dinner using 1 box of pasta and 1 jar of sauce. If pasta is sold in packages of 6 boxes and sauce is sold in packages of 3 jars, what is the least number of dinner that Manny can make without any supplies left over?
assuming Manny purchases packages of both pasta and sauce, then six dinners, using up
1 pkg pasta and 2 pkgs sauce
6: 6 12 18
————
3: 3 6 9
6 dinners
1 pack pasta
2 packs sauce
To find the least number of dinners that Manny can make without any supplies left over, we need to determine the least common multiple (LCM) of 6 and 3.
To find the LCM, we list the multiples of each number until we find a common multiple.
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
From the lists above, we can see that the LCM of 6 and 3 is 6.
This means that Manny can make 6 dinners with 6 boxes of pasta (6 x 1 box) and 6 jars of sauce (6 x 1 jar) without any supplies left over.