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Question: A patent attorney calculates the average number of claims in three patents, which contain 12, 18, and 24 claims. What is the average?
+ 36 + 49 + 64 + 81 + 100 + 121 + 144 = 620
Next, find the remainder when 620 is divided by 7. Divide 620 by 7:
Alternatively, compute each square modulo 7 and sum them:
Question: How many of the 200 smallest positive integers are congruent to 3 (mod 5)?
Question: What is the least common multiple of 18, 24, and 40?
The LCM is found by taking the highest power of each prime present:
Next, we find the remainder of 525 when divided by 7:
Now, find the remainder when 48032 is divided by 13:
The smallest two-digit number is 10. We check successive numbers until we find one that satisfies the condition: