Can Two Numbers Have 16 as Their HCF and 380 as Their LCM? Give Reason

Video Explanation

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Solution

Question: Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.

Step 1: Use the Relation Between HCF and LCM

For any two positive integers a and b,

a × b = HCF (a, b) × LCM (a, b)

Step 2: Substitute the Given Values

a × b = 16 × 380

a × b = 6080

Step 3: Check the Necessary Condition

For two numbers to exist, the LCM must be a multiple of the HCF.

But,

380 ÷ 16 = 23.75 (not an integer)

Step 4: Draw the Conclusion

Since 380 is not divisible by 16, such a pair of numbers cannot exist.

Final Answer

∴ No, two numbers cannot have 16 as their HCF and 380 as their LCM.

Conclusion

Thus, because the LCM must always be a multiple of the HCF and 380 is not divisible by 16, such two numbers are not possible.