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.
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