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Test the rule 'HCF × LCM = product of the two numbers' on 15 and 20. Which line below is correct?

Class 6Playing with NumbersPlaying with Numbers
  • AHCF 10 × LCM 30 = 300, which matches .
  • BHCF 5 × LCM 60 = 300, which matches .
  • CHCF 5 × LCM 60 = 300, but , so the rule fails.
  • DThe rule holds only when the two numbers are co-prime.

Step-by-Step Solution

Factors of 15: 1, 3, 5, 15; factors of 20: 1, 2, 4, 5, 10, 20 — so the HCF is 5. Multiples of 15: 15, 30, 45, 60; multiples of 20: 20, 40, 60 — so the LCM is 60. Then and . The traps: 10 is not a factor of 15 at all, is 300 and not 350, and the rule works for every pair of numbers, not only co-primes.
Answer: B) HCF 5 × LCM 60 = 300, which matches .

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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