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

15 minutes = 900 seconds

so basically, we would have to find the common multiples of 18 and 42....going all the way to 900

I am not gonna list all the multiples of 18 and 42.....but the common multiples of both are : 126,252,378,504,630,756,882 ...thats 7 numbers

therefore, he will do jumping jacks and whistle (at the same time ) 7 times during the 15 minute period

Answer 2

15 mins = 900 s

We need to find all common multiples of 18 and 42 less than or equal 900.
We'll find the least common multiple first.

18|2
9|3
3|3
1

42|2
21|3
7|7


`\text{lcm}(18,42)=2\cdot3^2\cdot7=126`

Now, we nned to find all multiples of 126 that are less than or equal 900.
Those are 126,252,378,504,630,756,882. There are 7 of those.
Therefore the answer is 7.