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Sonal is told that two numbers have HCF 8 and LCM 30. She says no such pair of numbers can exist. Is she right?

Class 6Playing with NumbersPlaying with Numbers
  • ANo — the numbers are 8 and 30.
  • BNo — the numbers are 2 and 120.
  • CYes — the LCM always has to be smaller than the HCF.
  • DYes — the HCF must divide the LCM, and 8 does not divide 30.

Step-by-Step Solution

The HCF divides both numbers and both numbers divide the LCM, so the HCF is always a factor of the LCM. Here 30 ÷ 8 is not exact, so the pair is impossible. The trap is the swapped statement — the LCM is never smaller than the HCF; it is at least as large as the bigger number.
Answer: D) Yes — the HCF must divide the LCM, and 8 does not divide 30.

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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