To Find The Smallest Three Digit Number Divisible By 8 9 And 10 We First Determine The Least Common Multiple Lcm Of These Numbers
I still remember the day I struggled to find the smallest three-digit number that was divisible by 8, 9, and 10. My math teacher had assigned it as homework, and I was determined to solve it, but it seemed like an impossible task. Little did I know, the key to solving this problem lay in understanding the concept of Least Common Multiple (LCM).
So, let's dive into the world of LCM and explore how it can help us find the smallest three-digit number divisible by 8, 9, and 10. To do this, we need to first determine the LCM of these numbers, which is the smallest number that is a multiple of all three. It's like finding the common ground between these numbers, and it's not as complicated as it sounds.
Understanding LCM
The LCM of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 can divide into evenly. Now, let's apply this concept to our problem and find the LCM of 8, 9, and 10.
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To find the LCM, we need to list the multiples of each number and find the smallest number that appears in all three lists. The multiples of 8 are 8, 16, 24, 32,..., the multiples of 9 are 9, 18, 27, 36,..., and the multiples of 10 are 10, 20, 30, 40,.... As we can see, the numbers are getting bigger and bigger, but we're looking for the smallest one that meets the criteria.
The Calculation
After listing the multiples, we can see that the smallest number that appears in all three lists is 360. This means that 360 is the LCM of 8, 9, and 10. However, we're looking for the smallest three-digit number that meets the criteria, so we need to find the smallest multiple of 360 that is greater than or equal to 100.
As it turns out, the smallest three-digit number divisible by 8, 9, and 10 is indeed 360, because it's the smallest multiple of the LCM that meets the criteria. And there you have it, folks, the answer to the problem that had been puzzling me for so long. I hope this explanation was helpful, and you now understand the concept of LCM and how to apply it to real-world problems.
