Find the Number Nearest to 110000 and Greater than 100000 Exactly Divisible by 8, 15 and 21
Video Explanation
Watch the video below to understand the complete solution step by step:
Solution
Question: Determine the number nearest to 110000 but greater than 100000, which is exactly divisible by each of 8, 15 and 21.
Step 1: Find the LCM of 8, 15 and 21
Prime factorisation:
8 = 23
15 = 3 × 5
21 = 3 × 7
LCM = 23 × 3 × 5 × 7
LCM = 840
Step 2: Find the Multiple of 840 Nearest to 110000
110000 ÷ 840 ≈ 130.95
Nearest integers are 130 and 131
840 × 130 = 109200
840 × 131 = 110040
Step 3: Choose the Required Number
109200 is less than 110000
110040 is greater than 100000 and nearest to 110000
Final Answer
∴ The number nearest to 110000 and greater than 100000, exactly divisible by 8, 15 and 21 is 110040.
Conclusion
Thus, by finding the LCM of 8, 15 and 21 and checking the nearest multiples, we get the required number as 110040.