Find the Value of a When LCM(a, 18) = 36 and HCF(a, 18) = 2

Video Explanation

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Solution

Question: If the LCM of a and 18 is 36 and the HCF of a and 18 is 2, then find a.

(a) 2    (b) 3    (c) 4    (d) 1

Important Property

For any two positive integers a and b:

a × b = LCM(a, b) × HCF(a, b)

Step 1: Apply the Formula

a × 18 = 36 × 2

a × 18 = 72

Step 2: Find the Value of a

a = 72 ÷ 18

a = 4

Final Answer

✔ The value of a is 4.

✔ Correct option: (c) 4

Conclusion

Thus, using the relationship between HCF and LCM, we find that the value of a is 4.