Question

Find the 4-digit smallest number which when divided by 12, 15, 25, 30 leaves no remainder? 1300 1400 1200​

Answer 1

Answer: 1200 is the 4-digit smallest number which divided by 12,15,25,30 leaving no remainder

Answer 2

Given: Numbers 12, 15, 25 and 30

To find: The smallest 4 digit number which when divided by given numbers leaves no remainder

Solution:

To find the smallest 4-digits numbers which is completely divisible by 12, 15, 25 and 30, first we need to calculate L.C.M of these numbers.

Using prime factorization method:

12 = 2 x 2 x 3

15 = 3 x 5

25 = 5 x 5

30 = 2 x 3 x 5

L.C.M = 2 x 2 x 3 x 5 x 5 = 300

[L.C.M is calculated by multiplying the maximum count of common factors of all the given numbers. Here, common factors are 2, 3 and 5. 2 appears maximum 2 times, 3 appears maximum 1 time and 5 appears maximum two times. So, they have been multiplied together to get the L.C.M]

Now, L.C.M is 300 but it's not a 4-digit number.

But, all the multiples of 300 will be completely divisible by given numbers.

Multiples of 300 are :-

300, 600, 900, 1200, 1500..and so on

The smallest 4-digit number is 1200.

Therefore, the desired smallest 4-digit number which when divided by 12, 15, 25 and 30 leaves no remainder is 1200.