Question

Find the least number which when divided by 15,20,35,45 leaves remainder 5 in each case

Answer 1

To find the least number which when divided by 15,20,35 and 45 gives remainder 5, we first have to find the least common multiple of 15,20,35 and 45.

LCM of 15,20,35,45 = LCM(15,20,35,45)

= 1260

So the number 1260 is the smallest number divisible by all 15,20,35 and 45.
So if we add 5 to 1260, i.e. 1260+5=1265, we get the smallest number which when divided by 15,20,35 and 45 would give a remainder 5, in each case.

So the required answer is 1265.