Question

Find the smallest four digit number which is exactly divisible by 12,16,24 and 36 with steps

Answer 1

Answer:

The smallest four digit number which is exactly divisible by 12,16,24 and 36 is 1008

Step-by-step explanation:

As per the data given in the question,

We have,

12,16,24,36

By prime factorization, we get

$12 = 2^{2} \times3\\16 = 2^{4}\\ 24= 2^{3} \times3\\36 = 2^{2} \times3^{2}$

So the least number which is divisible by all the numbers is

$N=2^{4} \times 3^{2} = 144$

So, 6N = 864

7N =1008

Hence, the smallest four digit number which is exactly divisible by 12,16,24 and 36 is 1008

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Answer 2

Answer:

The smallest four-digit number which is exactly divisible by 12,16,24 and 36  =  1008

Step-by-step explanation:

To find,

The smallest four-digit number which is exactly divisible by 12,16,24 and 36

Recall the concept

The numbers exactly divisible by any numbers will be a product of the LCM of the numbers

Solution:

The given numbers are 12,16,24 and 36

To find the LCM of 12,16,24 and 36

The prime factorization of the numbers are

12 = 2×2×3

16 = 2×2×2×2

24 = 2×2×2×3

36 = 2×2×3×3

The LCM of 12,16,24 and 36 = 2×2×2×2×3×3 = 144

The smallest four-digit number which is exactly divisible by 12,16,24 and 36 =  The least four-digit multiple of 144

To find the least four-digit multiple of 144

Since, $\frac{1000}{144}$ = 6.94,

The smallest four-digit multiple of 144 =  7 ×144 = 1008

∴The smallest four-digit number which is exactly divisible by 12,16,24 and 36  =  1008

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