Marta uses 1 piece of paper and 1 piece of ribbon to make kites. the paper comes in packs of 3 pieces and the ribbon comes in packs of 4 pieces. what is the least number of kites marta can make without any supplies left over?

Step-by-step explanation:

Givens:

If Martha needs 1 piece of paper and ribbon, then she need to use 4 packs of paper and 3 packs of ribbons, because when she uses one pack of paper, she use it all, but from the pack of ribbons, it remains some.

From the first pack Marta has 3 papers and 4 ribbons. So, she uses all 3 papers, and 3 ribbons, and there remains 1 ribbons without use.

From the second pack, Marta uses 3 papers but only 2 ribbons, because she also uses the one ribbon that left from the first pack. So, from the second pack, she only uses 2 ribbons, and there are 2 ribbons left.

From the third pack, she again uses all three papers, but only 1 ribbon, so there is three ribbons left.

From the fourth pack she uses three papers agains, but she doesn't need a new pack of ribbons, because she has three from the third pack.

Now, specifically, the least common number refers to the least common multiple of 3 and 4, which is 12, because if we write down the multiples for both numbers, we have:

3, 6, 9, 12, 15, ...

4, 8, 12, 16, 20,...

As you can see, the least common number is 12.

Therefore, the least number of kites Marta can make without any supplies left over is 12.

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