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Answer:
Step-by-step explanation:
To find the LCM of 1,2,12,30,84,165 you must first find the prime factors of 12,30,84 and 165
12| 2 30| 2 84| 2 165| 3
6 | 2 15 | 3 42| 2 55 | 5
3 | 3 5 | 5 21 | 3 11 | 11
1 1 7 | 7 1
1
Now we look for common and uncommon factors with their greatest exponent
LCM(1,2,12,30,84,165)
Common factors with their greatest exponent:
Uncommon factors with their greatest exponent:
Solution :
If is the total spending generated after n transactions, then
is the spending generated during the n-th transaction. Since the government spends D dollars, then
= D.
Then the second person will receive D dollars and spend dollars. Therefore,
. The next person will receive
dollars, which means they are spending
dollars. Therefore,
....
∴