Question

Find the least square number which is exactly divisible by $4,6,9,12$ and $14$

• A. $252$
• B. $504$
• C. $1008$
• D. $1764$

Answer 1

The correct option is D $1764$

The least number which is exactly divisible by each of the number 4,6,9,12 and 14 is their L.C.M
The L.C.M of 4,6,9,12 and 14 is 252.But $252=2\times 2\times 3\times 3\times 7=(2\times 2)\times (3\times 3)\times 7$
The last factor 7 has no pair, so in order to make 252 a perfect square , it must be multiplied with 7
So $252\times 7=1764=2\times 2\times 3\times 3\times 7\times 7$
Hence 1764 is the required number.