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What is the length of the longest tape that can measure both 5 m 40 cm and 7 m 20 cm an exact number of times?

Class 6Playing with NumbersPlaying with Numbers
  • A180 cm
  • B60 cm
  • C90 cm
  • D2,160 cm

Step-by-Step Solution

Work in centimetres: 540 and 720. Now and , so the HCF is cm. The tape then fits 3 times into 540 cm and 4 times into 720 cm. The traps 60 cm and 90 cm do measure both lengths, but they are not the longest tape that does; 2,160 cm is the LCM.
Answer: A) 180 cm

Key idea: HCF and LCM — the two ends of common ground

**HCF** (Highest Common Factor) is the biggest number that divides both numbers — it sits at the *small* end of common factors. **LCM** (Least Common Multiple) is the smallest number both numbers divide — it sits at the *small* end of common multiples (which is the *big* side of factors). For Class 6, the simplest method is listing: write all the factors (or first several multiples) of each number and pick the right one. Faster methods come in Class 7.

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