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Question from jeff, a parent:

find 6 consecutive multiples of 6 whose sum is the least common multiple of 13 and 18

Jeff,

I can see two ways to approach this problem. One is algebraic.

Since the 6 numbers are consecutive multiples of 6 you can write them as

6n, 6n + 6, 6n + 12, ... 6n + 30

The least common multiple of 13 and 18 ia 13 × 18 = 234 so

6n + 6n + 12 + ... + 6n + 30 = 234

Solve for n.

The second method is "guess-and-check".

The six numbers have a sum of 234 so their average is 234/6 = 39. Thus the 6 multiples of 6 are centered at 39. What are they?

I hope this helps,
Penny

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