Calculate the smallest integer, which is a multiple of 4, 6, and 10.?

Step-by-Step Solution

To find the smallest integer that is a multiple of 4, 6, and 10, we need to calculate the Least Common Multiple (LCM).

1. Prime Factorization:

   • Find the prime factors of each number:

     • 4 = 2 * 2 = 2^2

     • 6 = 2 * 3

     • 10 = 2 * 5

2. Determine the LCM:

   • The LCM is found by taking the highest power of each prime factor present in the numbers:

     • Prime factors involved: 2, 3, and 5.

     • Highest power of 2: 2^2 = 4

     • Highest power of 3: 3^1 = 3

     • Highest power of 5: 5^1 = 5

   • LCM = 4 * 3 * 5 = 60.

The smallest integer that is a multiple of 4, 6, and 10 is 60.