Question

Mr. Rr the Rreliable Rrobot has been programmed to whistle every $18$ seconds and do a jumping jack every $42$ seconds, starting from the moment he is turned on. (For example, he does his first jumping jack $42$ seconds after he is turned on.)

How many times during the first $15$ minutes after activation will Mr. Rr whistle and do a jumping jack at the same instant?

Answer 1

7 times during the first 15 minutes

Explanation:

Remember that

`1\ min=60\ sec`

so

`15\ min=15(60)=900\ sec`

Decompose the numbers 18 and 42 in prime factors

we know that

`18=(2)(3^2)`

`42=(2)(3)(7)`

Find the least common multiple (LCM)

The LCM is

`(2)(3^2)(7)=126\ sec`

we need to find all multiples of 126 that are less than or equal 900.

`126*1=126\ sec\\126*2=252\ sec\\126*3=378\ sec\\126*4=504\ sec\\126*5=630\ sec\\126*6=756\ sec\\126*7=882\ sec`

therefore

7 times during the first 15 minutes