Question

find the smallest number exactly divisible by 12,22,32,42​

Answer 1

Answer:

2

Step-by-step explanation:

lcm of 12,22,32,42 is 2

Answer 2

The smallest number divisible by 12,32,42 is its LCM which is 2016.

The prime factorization of 2016 is 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7.

Pick out the pairs in this step. They are 2 x 2 2 x 2 3 x 3.

2 and 7 are not in pairs. But if there is one more 2 and one more 7, both 2 and 7 can also be in pairs.

So the required numbers are one more 2 and one more 7. So it is 2 x 7 = 14.

Therefore, 2016 x 14 = 28224.

So the required square number is 28224. i.e. (168^2).