The number 3072 is divisible by both 6 and 8. what is the larger than 3072 that is also divisible by both 6 and 8?

To find a number larger than 3072 that is divisible by both 6 and 8, we first need to determine the least common multiple (LCM) of these two numbers.

Finding the LCM

The LCM of 6 and 8 can be calculated as follows:

• Factors of 6: 2 × 3
• Factors of 8: 2 × 2 × 2

The LCM takes the highest power of each prime factor:

• From 6: 2¹ and 3¹
• From 8: 2³

Thus, the LCM is:

LCM = 2³ × 3¹ = 24

Finding the Next Multiple

Now, we need to find the smallest multiple of 24 that is greater than 3072:

First, divide 3072 by 24:

3072 ÷ 24 = 128

This means 3072 is the 128th multiple of 24. To find the next multiple, we add 1:

Next multiple = 24 × 129 = 3104

Final Answer

The smallest number greater than 3072 that is divisible by both 6 and 8 is 3104.