Question

find the least 4 digit no. which is exactly divisible by 8,10and12​

Answer 1

Answer:

1200

Step-by-step explanation:

Answer 2

Answer:

1080

explanation :

Let’s do prime factorization for the three numbers to find the least common multiple (LCM) for the given numbers:

8 = 2 * 2 * 2

10 = 2 * 5

12 = 2 * 2 * 3

As far as 3 and 5 are odd numbers, we’ll have the following to construct the LCM for the three numbers:

2*2*2, the number’s divisible by 8

2*2*2*5 will make the number divisible by 10 (LCM for 8 and 10)

2*2*2*5*3 the number’s now divisible by 12 (LCM for 8, 10, 12)

So we have 2*2*2*3*5 = 120 and it’s the LCM of 8, 10 and 12.    

The smallest four digit number is 1000, right? :)

So now we have to find the smallest four digit number that is a multiple of 120, let’s go:

1000 / 120 = 8.33

8 < 8.333 < 9

8 * 120 = 960 (it is not a four digit number)

9 * 120 = 1080 (or 960 +120) which is a four digit number and it’s the smallest four digit number which is divisible by 8, 10 and 12.