Question

a piece of string can be cur into equal lengths, either 20 cm or 24 cm or 30cm long Find the length of the shortest piece of string for which this is possible.​

Answer 1

120 cm

Explanation:

this leads to the Least Common Multiple ( LCM ) also known as Lowest Common Multiple.

for example using prime factors :

20 = 2×2×5

24 = 2×2×2×3

30 = 2×3×5

LCM is the combination of the longest chains of the various prime factors :

LCM = 2×2×2×3×5 = 120

so, the shortest piece of string that allows all these cut variations is 120 cm long.