Given HCF and LCM of Two Numbers, Find the Other Number

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: The HCF of two numbers is 145 and their LCM is 2175. If one number is 725, find the other number.

Step 1: Use the Relation Between HCF and LCM

For any two positive integers a and b,

a × b = HCF (a, b) × LCM (a, b)

Step 2: Substitute the Given Values

Let the other number be x.

725 × x = 145 × 2175

Step 3: Find the Value of the Other Number

x = (145 × 2175) ÷ 725

x = (145 × 2175) ÷ (145 × 5)

x = 2175 ÷ 5

x = 435

Final Answer

∴ The other number is 435.

Conclusion

Thus, using the relation between HCF and LCM, we find that the other number corresponding to HCF 145 and LCM 2175 is 435.