highest common factor and lowest common multiple worded questions

Question

I've got this really confusing homework can someone plz help
The title of it is highest common factor and lowest common multiple worded questions

A) two hands move around a dial. The faster hand moves around in 24 seconds and the slower in 34 secs. If the two hands start together at the top of the dial, how many seconds does it take before they are at the top.

B) A floor is covered in square tiles. The floor measures 420cm x 810cm What is the largest size of square tile can be used to tile the floor without breaking any of the tiles?

C) A garden measures 31.5m by 29.4m. It is fenced in using posts which must be equal distance apart. what's the greatest distance apart the posts can be?

Plz help me it's due tomorrow and was set today

Answer 1

A)

The LCM, Least Common Multiple, must be for 24, 34, and 60.

The 60 because they have to meet up again at the top.

The prime factors are: 2³·3, 2·17, and 2²·3·5

The LCM is 2040.

The hands meet at the top after 2040 seconds or 34 minutes.

 

B)

The sides of the square must be the GCF, Greatest Common Factor of 420 and 810

The prime factos are: 2²·5·3·7, and 2·5·9·9

The GCF is 2

The largest the tiles can be are 2 cm x 2 cm.

 

C)

The distance between posts is the GCF, Greatest Common Factor, of 3150 cm and 2940 cm

The prime factors are 2²·5²·3², and 2²·5·17

The GFC is 20.

The farthest the post can be apart if 20 cm.