what is the shortest length of string that can be cut into all 5cm lengths, all 8cm lengths or all 10cm lengths?

This is geometry?

LCM of 5, 8, and 10 is 40.

Shortest length of string = 40 cm

Is this what you need?

To find the shortest length of string that can be cut into all 5cm, 8cm, or 10cm lengths, we need to find the least common multiple (LCM) of these three numbers.

One way to find the LCM is by listing the multiples of each number until we find a common multiple. Another method is to use prime factorization.

Let's use prime factorization to find the LCM of 5, 8, and 10:

Prime factorization of 5: 5 = 5^1
Prime factorization of 8: 8 = 2^3
Prime factorization of 10: 10 = 2^1 * 5^1

To find the LCM, we take the highest power of each prime factor that appears in any of the numbers. In this case, we have:

LCM = 2^3 * 5^1 = 8 * 5 = 40

Therefore, the shortest length of string that can be cut into all 5cm, 8cm, or 10cm lengths is 40cm.