🪢 Cutting three ropes into equal pieces

A closer look at one question · SMC 2024, Question 27 (bank id C2)

Kenny has 3 ropes: 24 cm, 60 cm and 96 cm. He wants to cut them into smaller pieces of EQUAL length, with nothing left over, and each piece as LONG as possible. How many pieces can he get altogether?

1 One piece length has to fit ALL three ropes exactly

So the piece length must DIVIDE 24, 60 and 96 exactly — and "as long as possible" means the biggest number that does. That is the Highest Common Factor.

2 Try 12 cm against each rope

24 cm
1212
60 cm
1212121212
96 cm
1212121212121212

12 cm fits every rope with nothing left over, and no bigger number works for all three — so 12 cm is the biggest piece length that is possible.

3 Count the pieces, rope by rope

rope÷ 12 cmpieces
24 cm24 ÷ 122
60 cm60 ÷ 125
96 cm96 ÷ 128
total2 + 5 + 815
15 pieces

The trap: answering 12 — that is the LENGTH of each piece, not how many there are. Read the question, not just the arithmetic you just did.