Find the LCM of a = pq² and b = p³q

Video Explanation

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Solution

Question: If two positive integers a and b are expressible in the form

a = p q²
b = p³ q

where p and q are prime numbers, find LCM(a, b).

Step 1: Write Prime Powers

a = p¹ × q²

b = p³ × q¹

Step 2: Apply the Rule for LCM

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

Highest power of p = 3

Highest power of q = 2

Step 3: Write the LCM

LCM(a, b) = p³ q²

Final Answer

✔ LCM(a, b) = p³ q²

Conclusion

Thus, by taking the highest powers of the prime factors p and q, the LCM of the given numbers is p³ q².