Manny makes dinner using 1 box 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 dinners that Manny can make without any leftovers?
The least common multiple of 6 and 3 is 6.
9+10=
21. B. R. U. H.
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To figure out the least number of dinners Manny can make without any leftovers, let's start by considering the quantities of pasta and sauce available.
Pasta is sold in packages of 6 boxes, and Manny has 1 box. This means he has 1/6 of a package of pasta.
Sauce is sold in packages of 3 jars, and Manny has 1 jar. This means he has 1/3 of a package of sauce.
Now we need to determine how many dinners can be made with these quantities. Since each dinner requires 1 box of pasta and 1 jar of sauce, we need to find the lowest common multiple (LCM) of 1/6 and 1/3.
To find the LCM, we need to find the least common denominator (LCD) of 6 and 3, which is 6. Therefore, the LCM of 1/6 and 1/3 is 1/6.
Since Manny has 1/6 of a package of pasta and 1/3 of a package of sauce, the LCM (1/6) represents the number of complete dinners that can be made.
Therefore, Manny can make 1 dinner without any leftovers.