Can two numbers have $18$ as their HCF and $380$ as their LCM? Give reasons.
Step-by-Step Solution
Key Concept: HCF must always divide LCM completely.
We divide $380$ by $18$: $380 / 18 = 21.11$ (remainder $2$). [1.0 Mark]
Since HCF ($18$) does not divide LCM ($380$) completely, NO two numbers can have HCF $18$ and LCM $380$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Dividing 380 by 18: 1.0 Mark
Concluding NO because HCF must divide LCM: 1.0 Mark
Correct Answer: