The aluminum pipe must be cut into equal parts without waste. 1) What is the smallest length of the pipe so that

The aluminum pipe must be cut into equal parts without waste. 1) What is the smallest length of the pipe so that it can be cut both into 6m pieces and into 8m pieces? 2) into how many parts of the longest length can two pipes 35m and 42m long be cut?

1) To find the smallest pipe length, you need to find the LCM (least common multiple) of 6 and 8.

6 = 2 * 3; 8 = 2 * 2 * 2.

LCM (6 and 8) = 2 * 3 * 2 * 2 = 24.

Answer: The pipe must be 24 m long.

2) To find the longest part of the pipe, find the GCD (greatest common denominator) of 35 and 42.

35 = 5 * 7; 42 = 7 * 3 * 2.

GCD (35 and 42) = 7. That is, the maximum length of a part of the pipe is 7 m.

The 35 m pipe must be cut into 35: 7 = 5 pieces.

The 42 m pipe must be cut into 42: 7 = 6 pieces.