Question

A carpenter has boards of lengths 24, 36, and 42 inches that must be cut into smaller boards of equal length, with no scrap wood left over. What is the longest length of boards he can cut?

2 inches.
4 inches.
6 inches.
12 inches.

Answer 1

Option C - 6 inches.

Explanation:

Given : A carpenter has boards of lengths 24, 36, and 42 inches that must be cut into smaller boards of equal length, with no scrap wood left over.

To find : What is the longest length of boards he can cut?

Solution : A carpenter has boards of lengths 24, 36, and 42 inches that must be cut into smaller boards of equal length.

For the equal length we have to find the HCF of the given dimension

As HCF is the highest common factor which divide all dimension in equal length.

To find HCF factorise each dimension

`24=2*2*2*3\\36=2*2*3*3\\42=2*3*7`

`HCF(24,36,42)=2* 3=6`

So, The length of boards he cut is of 6 inches.

Therefore, Option C is correct.

Answer 2

42-24 = 18

36-24 = 12

18-12 = 6

24/6 = 4

36/6 = 6

42/6 = 7

longest length would be 6 inches