Find the Smallest Number Which Is Divisible by Both 306 and 657

Video Explanation

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

Solution

Question: Write the smallest number which is divisible by both 306 and 657.

Step 1: Identify the Mathematical Concept

The smallest number which is divisible by two given numbers is their LCM (Least Common Multiple).

Step 2: Use the Relation Between LCM and HCF

For any two positive integers a and b,

a × b = LCM (a, b) × HCF (a, b)

From the previous result,

HCF (306, 657) = 9

Step 3: Calculate the LCM

LCM (306, 657) = (306 × 657) ÷ 9

LCM (306, 657) = 20142

Final Answer

∴ The smallest number which is divisible by both 306 and 657 is 20142.

Conclusion

Thus, the required smallest number divisible by 306 and 657 is their LCM, which is 20142.