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, .....
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