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Introduction
Finding the Lowest Common Denominator
Arithmetic Sequence and Series
Finding Unit Digits of x^n
  FINDING THE LOWEST COMMON DENOMINATOR (LCD)
Conclusion:

Every 24 items were checked by both Joe and Sally.

Therefore, if on a given day 1,000 items passed by both of them and Joe checked every 8th item and sally checked every 12th item, then


But there are only finished items on the assembly line, so 41 items were checked by both of them.
Conclusion
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