SOLUTION: A grasshopper and a frog start together and jump along the same path. The grasshopper always jumps 12 cm and the frog always jumps 15cm. Will they ever land on the same spot again?

Question 956331: A grasshopper and a frog start together and jump along the same path. The grasshopper always jumps 12 cm and the frog always jumps 15cm. Will they ever land on the same spot again? Where?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
definitely.

look for the least common multiple of 12 and 15.

12 = 3 * 4
15 = 3 * 5
combine the two 3's into one 3 because they're common.
keep the 4 and the 5 because they're not common.
least common multiple is 3 * 4 * 5 = 60
they will land on the spot again every 60 cm.

note that i could have made 12 = 3 * 2 * 2 but it was not necessary because neither 2 nor 4 are common to 5.

i would have gotten 3 * 2 * 2 * 5 which is the same as 3 * 4 * 5 which is equal to 60.

the grasshopper jumps on spots 12, 24, 36, 48, 60, .....
the frog jumps on spots 15, 30, 45, 60,

they will land on the same spot on:

60, 120, 180, 240, 300, .....

RELATED QUESTIONS
A rabbit and a frog jump toward each other. The rabbit takes two jumps for every three... (answered by ikleyn)

A frog jumped 20 centimeters away from a door and then jumps again 15 centimeters away... (answered by greenestamps)

A researcher studying frogs is investigating the distance that a certain species of frog... (answered by Boreal)

in a computer game room there is a mechanical grasshopper in a glasscage. The grasshopper (answered by Theo)

A frog jumps and takes 2 seconds to land. The path of the frog’s flight is best modeled (answered by Alan3354)

Of the water lilies in the pond, 43% are yellow. The others are white. A frog randomly... (answered by Edwin McCravy)

A frog jumps from a rock to the shore of a pond. Its path is given by the equation:y =... (answered by macston)

A frog leaps 2 feet. The highest point in the jump is 6 inches. Assume the frog starts at (answered by josmiceli)

A frog leaps 2 feet horizontally. The highest point in the jump is foot. Assume the frog (answered by Alan3354)