Help me with this math problem please.

Question

Filter A is cleaned immediately after it has attracted 24 grams of dust. Filter B is cleaned immediately after it has attracted 30 grams of dust. Both filters are installed at the same time and receive the same amount of dust. After how many grams of dust will both filters be cleaned at exactly the same time for the first time?

 

A. 60 grams 

B. 120 grams

C. 180 grams

D. 240 grams

Answer 1

Hi, Fabian.

 

So, to solve this problem you need to find the least common multiple of the two numbers. 

An easy way to do this is to find the multiples of each number and see when they're the same.

 

Filter A  is cleaned after every 24 grams of dust

 

Filter A : 24, 48, 72, 96, 120.....

 

Filter B is cleaned after every 30 grams of dust

 

Filter B : 30, 60, 90, 120......

 

As you can see, they both are cleaned at 120 grams of dust..

 

 

Answer 2

24 x 5 = 120

 

120 is divisible by 30  120/30 = 4

 

so ,the answer is 120 g