Find the Value of n Using LCM of a, b and c

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: If

a = 2³ × 3
b = 2 × 3 × 5
c = 3ⁿ × 5

and

LCM (a, b, c) = 2³ × 3² × 5

find the value of n.

Step 1: Write Prime Factorisations

a = 2³ × 3¹

b = 2¹ × 3¹ × 5¹

c = 3ⁿ × 5¹

Step 2: Use the Rule for LCM

The LCM is obtained by taking the highest power of each prime appearing in the numbers.

Step 3: Compare Powers of 3

Power of 3 in a = 1

Power of 3 in b = 1

Power of 3 in c = n

Given that the power of 3 in the LCM is 2.

∴ n = 2

Final Answer

✔ The value of n is 2.

Conclusion

Thus, by comparing the highest powers of prime factors in the LCM, we find that n = 2.