Find the number closest to 1000 and smaller than it that is divisible by both 5 and 6

Answer

To find the number closest to 1000 that is smaller than it and divisible by both 5 and 6, we can follow these steps:

### Step 1: Find the LCM of 5 and 6
The first step is to determine the least common multiple (LCM) of the two numbers, 5 and 6.

- The prime factors of 5 are just 5.
- The prime factors of 6 are 2 and 3.

To find the LCM, we take the highest power of each prime factor:
- LCM(5, 6) = 2^1 * 3^1 * 5^1 = 30.

### Step 2: Divide 1000 by the LCM
Next, we divide 1000 by the LCM we found in the previous step.

- 1000 ÷ 30 = 33.33 (approximately).

### Step 3: Find the largest whole number less than the result
Since we need a whole number that is smaller than the result, we take the integer part of the division.

- The largest whole number less than 33.33 is 33.

### Step 4: Multiply the whole number by the LCM
Now, we multiply this whole number by the LCM to find the closest number smaller than 1000.

- 33 * 30 = 990.

### Step 5: Verify divisibility
Finally, we check if 990 is divisible by both 5 and 6.

- 990 ÷ 5 = 198 (which is a whole number).
- 990 ÷ 6 = 165 (which is also a whole number).

Since 990 is divisible by both 5 and 6, we confirm that it is the correct answer.

### Conclusion
The number closest to 1000 that is smaller than it and divisible by both 5 and 6 is **990**.

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