Find the least five-digit number which can be divided by 8, 12, 16 and 20 leaving remainders 1. 5, 9 and 13, respectively.
Created: 2 years ago |
Updated: 3 months ago
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To find the least five-digit number that satisfies these conditions, you need to find the least common multiple (LCM) of 8, 12, 16, and 20, and then add 1, 5, 9, and 13 to it. Here's the step-by-step process:
- Find the LCM of 8, 12, 16, and 20:
LCM(8, 12, 16, 20) = 240
- Add the remainders 1, 5, 9, and 13 to the LCM:
240 + 1 = 241 240 + 5 = 245 240 + 9 = 249 240 + 13 = 253
- Now, find the least five-digit number among these values:
The least five-digit number is 10,000.
- Check which of the values (241, 245, 249, 253) is the smallest one that is greater than or equal to 10,000:
The smallest value that satisfies this condition is 10,073.
So, the least five-digit number that can be divided by 8, 12, 16, and 20, leaving the remainders 1, 5, 9, and 13, respectively, is 10,073.
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