Question

Find the smallest 4 digit number which is completely divisible by 24,25,60​

Answer 1

Answer:

We can solve this answer easily by taking LCM of 24,25,60

Step-by-step explanation:

So , LCM of 24,25,60

2    24,25,60

3    12,25,30

2    4,25,10

5    2,25,5

      2,5,1

2 x 3 x 2 x 5 x 2 x 5 x 1 =600

therefore the smallest 4 digit number which is completely divisible by 24,25,60 is 600 .

hope you understood the answer

thank you.

Answer 2

The smallest 4-digit number which is completely divisible by 24, 25 and 60 is 1200.

Given:

The number is completely divisible by 24, 25 and 60.

To Find:

The smallest 4-digit number that is divisible by 24, 25 and 60.

Solution:

To get to the answer, you need to compute the lowest common multiple (LCM) of the given numbers.

To compute the LCM, we can proceed as follows -

24= 2×2×2×3

25= 5×5

60= 2×2×3×5

Now, we multiply each prime factor the greatest number of times it occurs in either number​'s expansion.

LCM= 5×2×2×3×2×5= 600

600 is the smallest number which is divisible by 24, 25 and 60 but it is a 3-digit number.

So, to get the nearest 4-digit number we find the multiple of LCM.

1200 is the multiple of 600.

Hence, the smallest 4-digit number which is completely divisible by 24, 25 and 60 is 1200.

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