Answer:
The smallest three-digit number that is divisible by 3, 5, and 20 is 120.
Step-by-step explanation:
One way to solve this is to determine first the least common multiple of 3, 5, and 20. We can use the prime factorization method to determine the least common multiple of a set of numbers. In this case, the numbers are 3, 5, and 20.
Some Types of Divisors
- Least common multiple
- Greatest common multiple
- Least common divisor
- Greatest common divisor
Solution:
Let's use the prime factorization to determine the Least Common Multiple of 3, 5, and 20.
[tex]\begin{array}{ccccccccccc}5& \rightarrow& 5\\3&\rightarrow&&&3\\20&\rightarrow&5&\cdot&&&2&\cdot&2 \\\\&\rightarrow&5&\times&3&\times&2&\times&2&=&60\end{array}[/tex]
This means to say that the least common multiple of 3, 5, and 20 is 60. Given this fact, it also follows that all multiples of 60, such as 60, 120, 180, 240, 300, and so on, are divisible by 3, 5, and 20.
From this list, 60, 120, 180, 240, 300, and so on. These are all divisible by 3, 5, and 20, and it clearly shows that the smallest three-digit number is 120.
Thus, the answer is 120.
To learn more about divisibility, go to
- Meaning of least common multiple: https://brainly.ph/question/179194
- Least common multiple of 24, 45, 63: https://brainly.ph/question/1757416
- Least common multiple of 6 and 8: https://brainly.ph/question/6443339
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