correct answer is: a) 364

Explanation

First we find the LCM of 9,12 and 15.
\rightarrow LCM of 9,12 and 15 is =3\times3\times4\times5
\rightarrow 180.
Now we add 4 to 180.
\therefore\left(180+4\right)=184 is the number which leaves a remainder 4 in each case when divided by 9,12 and 15.
But, 184 is not divisible by 7.
So, we move to the next multiple of 180, which is 360.
Now we add 4 to 360.
\therefore\left(360+4\right)=364 is the number which leaves a remainder 4 in each case when divided by 9,12 and 15.
And, 364 is also divisible by 7, Like \large\left(\frac{364}{7}\right)\normalsize=52.
Hence, 364 is the least number that divisible by 7 and leaves a remainder 4 in each case when divided by 9,12 and 15.
Ans: The least number is 364.

Another form of this specific math question exists:

1. What is the lowest non negative integer that is a multiple of 7 and gives a remainder of 4 when divided by 9, 12 and 15?
2. Identify the smallest natural number that satisfies the conditions of being divisible by 7 while leaving a remainder of 4 when divided by 9, 12 and 15.
3. What is the minimum whole number that, when divided by 7, yields a remainder of 4 and also leaves a remainder of 4 when divided by 9, 12 and 15?