Final answer:
To find the smallest number divisible by 28, 35, and 56, we find the LCM (least common multiple) of these numbers, which is 280.
Step-by-step explanation:
To find the smallest number that is divisible by 28, 35, and 56, we need to find the least common multiple (LCM) of these three numbers. LCM is the smallest number that is divisible by all the given numbers.
Let's find the LCM of 28, 35, and 56:
- Prime factors of 28 are 2 * 2 * 7
- Prime factors of 35 are 5 * 7
- Prime factors of 56 are 2 * 2 * 2 * 7
The LCM is obtained by taking the highest power of each prime factor that occurs in any of the numbers. Therefore, the LCM of 28, 35, and 56 is 2 * 2 * 2 * 7 * 5 = 280.
So, the smallest number exactly divisible by 28, 35, and 56 is 280.
Learn more about Finding the LCM of numbers