19. Three mark exercise problems IV

1. Find the length of the longest rope that can be used to measure exactly the ropes of length $1 \ m \ 20 \ cm$, $3 \ m \ 60 \ cm$ and $4m$.

 

 

Length of the longest rope $=$ 20 m40 m20 cm40 cm

 

2. In an apartment consisting of $108$ floors, two lifts $A$ and $B$ starting from the ground floor, stop at every $3^{rd}$ and $5^{th}$ floors respectively. On which floors, will both of them stop together?

 

 

$A$ and $B$ meet at the floors 8, 16, 24, 32, 40, 48, 60, 72, 80, 88, 96, 1043, 5, 7, 9, 11, 13, 15, ....., 105, 10715, 30, 45, 60, 75, 90, 105