MediumMathematicsHigh School (9–10)GeneralNumber Systems › Divisibility, HCF and LCMNumericalreal-life
Three tanks hold 238 litres, 357 litres and 476 litres of water.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Three tanks hold litres, litres and litres of water. What is the largest jug that can measure the water of each tank exactly, a whole number of times? How many jugfuls are there in all?
Need a reminder? The key ideaShow
The largest equal size that fits exactly into some amounts is their HCF. The first time things happen together again is the LCM of their times. With remainders, take them away first (HCF) or add one to the LCM. Euclid's method: gives HCF HCF.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Factorise. , , .
Step 2. HCF. litres.
Step 3. Count. jugfuls.
Answer: a jug of litres, and jugfuls in all.
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