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A verandah floor is 12 m long and 9 m wide, and it is to be paved with equal square tiles. What is the biggest tile side that fits both measurements exactly, with no tile cut?

Class 6Playing with NumbersPlaying with Numbers
  • A1 m
  • B3 m
  • C4 m
  • D36 m

Step-by-Step Solution

The tile side must divide both 12 and 9 exactly and be as large as possible — that is the HCF. Factors of 12: 1, 2, 3, 4, 6, 12; factors of 9: 1, 3, 9; the highest shared one is 3. The trap is 36, the LCM — a 36 m tile is far bigger than the whole verandah. 4 divides 12 but not 9.
Answer: B) 3 m

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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