Finding the Least Common Multiple (LCM) of Given Numbers

To solve this problem, we need to find the least common multiple of the given numbers (6, 9, 15, and 18) and then add 4 to it to get the desired number. We can find the LCM by prime factorization or by listing multiples.

Prime Factorization Method:

- Prime factorize each number: 6 = 2 x 3, 9 = 3 x 3, 15 = 3 x 5, 18 = 2 x 3 x 3
- Write down the highest power of each prime factor: 2 x 3 x 3 x 5 = 90
- Therefore, the LCM of 6, 9, 15, and 18 is 90

Adding the Remainder:

- Add the remainder of 4 to the LCM: 90 + 4 = 94
- Therefore, the least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15, and 18 is 94

Listing Multiples Method:

- List the multiples of the largest number (18) until we find a multiple that leaves a remainder of 4 when divided by the other numbers: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360, 378, 396, 414, 432, 450, 468, 486, 504, 522, 540, 558, 576, 594, 612, 630, 648, 666, 684, 702, 720, 738, 756, 774, 792, 810, 828, 846, 864, 882, 900, 918, 936, 954, 972, 990, 1008, 1026, 1044, 1062, 1080, 1098, 1116, 1134, 1152
- The first multiple that leaves a remainder of 4 when divided by 6, 9, 15, and 18 is 90
- Therefore, the least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15, and 18 is 90 + 4 = 94

Final Answer:

Therefore, option 'D' (364) is incorrect and the correct answer is option 'B' (94).