If Mary inspects every sixth calculator and Nancy inspects every fifth calculator, which calculator will
be the first that they both inspect?
The thirtieth calculator
The calculator they both inspect is the least common multiple of 6 and 5.
The LCM of 6 and 5 equals 30.
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To find the first calculator that both Mary and Nancy will inspect, we need to determine the first common multiple of the numbers 6 and 5.
One way to do this is by listing the multiples of each number until we find a common multiple.
For Mary inspecting every sixth calculator: 6, 12, 18, 24, 30,...
For Nancy inspecting every fifth calculator: 5, 10, 15, 20, 25, 30,...
As we can see, the first common multiple of 6 and 5 is 30 because it appears in both lists. Therefore, the first calculator that both Mary and Nancy will inspect is the 30th calculator.