The smallest number of five digits exactly divisible by 476 isOptions47600104761047210000
Question
The smallest number of five digits exactly divisible by 476 is:
- Options
- 47600
- 10476
- 10000
Solution
To find the smallest number of five digits that is exactly divisible by 476, we can start by finding the least common multiple (LCM) of 476 and 10,000.
Step 1: Prime factorize 476: 476 = 2^2 * 7 * 17
Step 2: Prime factorize 10,000: 10,000 = 2^4 * 5^4
Step 3: Find the LCM by taking the highest power of each prime factor: LCM = 2^4 * 5^4 * 7 * 17
Step 4: Calculate the LCM: LCM = 16 * 625 * 7 * 17 = 476,000
Therefore, the smallest number of five digits exactly divisible by 476 is 476,000.
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