Question

The smallest 4 digit number divisible by 24, 15 and 36 is

Plz ans​

Answer 1

Answer:

We have to first find the LCM of 18, 24 and 36:

18 = 2 3 3

24 = 2 2 2 3

36 = 2 2 3 3

LCM = 2 2 2 3 3 = 72

So, LCM of 18, 24 and 36 is 72. But we want the least 4 digit number, which is exactly divisible by 18, 24 and 36.

Smallest 4 digit number = 1000.

Now,

1000 = (13 72) + 64

Next higher quotient is 14.

Now,

1000 = (13 72) + 64

Next higher quotient is 14.

So, the required number = 14 72 = 1008

Hence, the required number is 1008, which is exactly divisible by 18, 24 and 36.

Answer 2

SOLUTION

TO DETERMINE

The smallest 4 digit number divisible by 24 , 15 and 36

CONCEPT TO BE IMPLEMENTED

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

EVALUATION

Here the given numbers are 24 , 15 and 36

We now prime factorise the given numbers

24 = 2 × 2 × 2 × 3

15 = 3 × 5

36 = 2 × 2 × 3 × 3

LCM

= 2 × 2 × 2 × 3 × 3 × 5

= 360

Now

360 × 1 = 360 : which is 3 digit number

360 × 2 = 720 : which is 3 digit number

360 × 3 = 1080 : which is 4 digit number

So the required number = 1080

FINAL ANSWER

The smallest 4 digit number divisible by 24, 15 and 36 = 1080

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