Find the LCM and HCF of 336 and 54 and Verify LCM × HCF = Product of the Integers

Video Explanation

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Solution

Question: Find the LCM and HCF of the pair of integers 336 and 54 and verify that LCM × HCF = Product of the integers.

Step 1: Find the HCF of 336 and 54

Prime factorisation:

336 = 2 × 2 × 2 × 2 × 3 × 7 = 2⁴ × 3 × 7
54 = 2 × 3 × 3 × 3 = 2 × 3³

Common factors = 2 × 3

∴ HCF (336, 54) = 6

Step 2: Find the LCM of 336 and 54

LCM is the product of the highest powers of all prime factors:

LCM = 2⁴ × 3³ × 7

LCM = 3024

Step 3: Verify the Given Relation

LCM × HCF = 3024 × 6 = 18144

Product of the given integers = 336 × 54 = 18144

Since both values are equal, the relation is verified.

Final Answer

HCF of 336 and 54 = 6
LCM of 336 and 54 = 3024

∴ LCM × HCF = Product of the integers is verified.

Conclusion

Thus, for the integers 336 and 54, the product of their LCM and HCF is equal to the product of the integers themselves.