A rabbit and a frog

Number Theory Level 1

A rabbit and a frog are comparing their jumping ability. The rabbit can leap a horizontal distance of 54 cm the frog only 42 cm. What is the minimum distance they can both caver in an exact number of jumps?

379 cm 378 cm 298 cm 388 cm

Zoha Abid by Zoha Abid , 32, Pakistan

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8 solutions

Khadijat Oyeleye
Mar 1, 2014

Basically LCM of 54 and 42 which is 378 cm

Simple.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

we will only find their LCM;

Sol'n; (factoring) 

  54 = (9)(6)

  42 = (7)(6)

as we can see, (6) is common in both,so we will only take only one (6).. then, multiply to get the LCM,

LCM = 9 • 7 • 6 

      = 9 • 42

LCM = 378

that's all ..!! correct me if i'm wrong ^_^ thank you ;)

Jay Dave MU - 7 years, 3 months ago
Kshitij Tripathi
Feb 28, 2014

Take the L.C.M of the maximum heights which the two can jump. Height(Rabbit)=54 cm Height(Frog)=42 cm L.C.M of 54 and 42=378 Hence, 378 cm is the distance required

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Adrian Ma
Feb 19, 2019

Factorizing both, to give (2,3,3,3) and (2,3,7) respectively, we know the answer must be divisible by 2,3 and 7. Then we take advantage of the fact that it is multiple choice. ;). The only possible answer is 378.

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LCM(54,42) =378

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Siddhant Mahurkar
Apr 14, 2014

54=2x3x3x3 42=2x3x7 LCM=2x3x3x3x7=378

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Gaurav Singh
Mar 21, 2014

Basically LCM of 54 and 42 which is 378 cm

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Ashtik Mahapatra
Mar 20, 2014

simole take the lcm of 54 and 42

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Shreyas Shastry
Mar 1, 2014

just take the L.C.M of both the numbers 54 and 42 it comes to 378

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