Question

A Boy Saves Rs 4.65 daily . The least number of days in which he will be able to save exact number of repees​

Answer 1

Answer: 20 days

To find the least number of days to make the saving exact we must divide the total paisa the boy saved by his saving per day. Therefore, the least number of days in which he will be also to save an exact number of rupees is 20 day

Step-by-step explanation:

Complete step-by-step answer: It is given that the boy saves Rs 4.65 daily.

Rs.4.65= 465paisa

First see the number 4.65.

If we multiply it by any single number1,2,3,4,…8,9

, we will get a number with a decimal point.

Let us take the number 10 then, 4.65×10=46.50

which is also not an exact number.

The exact number of rupees will be multiple of 100

So, let us find the least common multiple of 465 and 100.

To find the least common multiple of both the numbers we should prime factorize them.

The prime factorization of,

100=2×2×5×5

465=3×5×31

Least common multiple of 465 and 100 is 2×2×5×3×5×31=9300

Thus, the boy saves 9300paisa=Rs93

To find the least number of days to make the saving exact we must divide the total paisa the boy saved by his saving per day.

That is the least number of days required to save 9300 paisa = 9300465=20days

Therefore, the least number of days in which he will be also to save an exact number of rupees is 20 days.

Note: LCM: The least common multiple of two integers a and b, usually denoted by

lcm(a,b)

, is the smallest positive integer that is divisible by both “a” and “b”.

Here we do not use the greatest common divisor to solve the problem because we have to find the least number of days.

Exact number is the whole number which does not have any decimal places.

We have used Rs.1=100paisa