Discussion
Three measuring jars have the capabilities of 15 ml, 50 ml and 30 ml. what is the least capacity which can be perfectly measured by any of the measuring jars?
Answer: C
The least capacity is 150 ml.
A quantity that each jar can measure exactly, in whole fillings, must be a multiple of 15, 50 and 30, so the least such quantity is their least common multiple:
\[ \begin{aligned} 15 &= 3 \times 5, \quad 30 = 2 \times 3 \times 5, \quad 50 = 2 \times 5^{2} \\ \text{LCM} &= 2 \times 3 \times 5^{2} = 150 \end{aligned} \]
150 ml is 10 fillings of the 15 ml jar, 5 of the 30 ml and 3 of the 50 ml. 100 is not a multiple of 15 or 30, and 75 is not a multiple of 50 or 30. 450 is a common multiple but not the least.
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