Find the LCM of 26 and 169 When Their HCF Is 13

Video Explanation

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Solution

Question: If HCF (26, 169) = 13, then LCM (26, 169) is:

(a) 26    (b) 52    (c) 338    (d) 13

Important Property

For any two positive integers a and b:

a × b = HCF(a, b) × LCM(a, b)

Step 1: Substitute the Given Values

26 × 169 = 13 × LCM

Step 2: Solve for LCM

LCM = (26 × 169) ÷ 13

LCM = 26 × 13

LCM = 338

Final Answer

✔ LCM (26, 169) = 338

✔ Correct option: (c) 338

Conclusion

Thus, using the relation between HCF and LCM, we find that the LCM of 26 and 169 is 338.