Question

The lengths of three strings were 60m, 72m and 168  m.  Pieces of string of equal  length were cut from  the three strings.   Calculate  the  least number of pieces obtained. ​

Answer 1

Total 25 strings each of 12 cm is obtained from the given strings.

Explanation:

The given length of the three strings are : 60 cm, 72 cm and 168 cm

On Prime Factorization of the given terms, we get:

60 = 2 x 2 x 3 x 5

72 = 2 x 2 x 2 x 3 x 3

168 = 2 x 2 x 2 x 3 x 7

The common factors to all these three terms is 2 x 2 x 3 = 12

So, from each string strings of length 12 cm can be cut.

Now, 60 ÷ 12 = 5

So, 5 strings of cut from this of equal length.

72 ÷ 12 = 6

So, 6 strings of cut from this of equal length.

168 ÷ 12 = 14

So, 14 strings of cut from this of equal length.

⇒Total number of strings of 12 cm = 5 + 6 + 14 = 25 strings

Hence, total 25 strings each of 12 cm is obtained from the given strings.