Find the number where the integers are multiples of 2 and 5

Answer 1

To find numbers that are multiples of both 2 and 5, we need to determine the least common multiple (LCM) of these two numbers.

1. Find the LCM of 2 and 5:

   • The prime factorization of 2 is \(2^1\).
   • The prime factorization of 5 is \(5^1\).
   • The LCM is found by taking the highest power of each prime: \[ \text{LCM}(2, 5) = 2^1 \times 5^1 = 10. \]

2. Generation of multiples:

   • The multiples of 10 (LCM) are \(10, 20, 30, 40, \ldots\), and so on. Each of these numbers is a multiple of both 2 and 5.

In conclusion, the numbers that are multiples of both 2 and 5 include \(10, 20, 30, 40,\) and any other positive integer that can be expressed as \(10n\) where \(n\) is a positive integer.