Question

Which is the smallest number which when divided by 25 and 30 leaves exactly 5 as remainder in both cases tell me the method and answer

Answer 1

25=5×5
30=2×3×5

LCM(25,30)= Product of greatest of each factor of the given numbers
=->2×3×5×5 = 150

Now the required number is 150+5 = 155 Ans.

Answer 2

The smallest number is 155, which is divisible by 25 and 30 and leaves the remainder as 5.

Given,

The number is divisible by 25 and 30.

It leaves 5 as the remainder.

Solution,

Let the smallest number be x.

If it leaves 5 as the remainder,

then,

The number is x+5.

So,

In this question, we have to take the LCM of the numbers.

So, let's understand the concept of LCM.

LCM stands for Least Common Multiple

In mathematics, LCM refers to the process of finding the smallest common multiple between two or more numbers. Common multiples are numbers that are multiples of two or more numbers.

Let's take the LCM of 25 and 30.

25 = 5 × 5.

30 = 2 × 3 × 5.

The LCM of 25 and 30 = 2 × 3 × 5 × 5 = 150

Then,

x = 150

The smallest number = x+5

= 150 + 5

= 155.

The smallest number is 155, which is divisible by 25 and 30 and leaves the remainder as 5.

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