possibility

Question

Q. What is the lowest possible number of marbles can be distributed evenly among 6 or 20 people

Q2. The Lollies are between 100 and 200 and can be divisible by 4 and 7?

Q3.Last year both comets XS and AE passed to Earth . XS returns to Earth every 7 years. While AE returns to Earth every 8 yrs. If this year is 2000. In which year will both comets next pass close to Earth?

 

Q4. Rachel watered one of her plants every 10 days and another 12 dyas. If she watered both plants today, in how many days’ time will Rachel water both plants on the say days?

Answer 1

These questions all involve finding the LCM or Least Common Multiple of 2 numbers.  There are different ways to find the LCM and I don't know how you were taught to do it, but one way is to use the formula 

 

LCM(a,b) = (a*b) / GCD(a,b) 

 

where GCD(a,b) is the Greatest Common Divisor of a and b.  

 

So for Q1, GCD(6,20) = 2 so LCM(6,20) = 120/2 = 60 is the lowest number of marbles that can be distributed evenly among 6 or 20 people.  

 

For Q2, GCD(4,7) = 1 so LCM(4,7) = 4*7/1 = 28.  You can write down the multiples of 28 (28,56,84,112,140,168,196,224) and pick the ones that are between 100 and 200 (112,140,168,196). 

 

For Q3, GCD(7,8) = 1 so LCM(7,8) = 56.  So 2056 is the next year both comets will pass close to Earth.  

 

For Q4, GCD(10,12) = 2 so LCM(10,12) = 120/2 = 60.  So Rachel will water both plants on the same day again in 60 days.