Find the least number which when divided by `12, 16, 24` and `36` leaves a remainder `7` in each case.

Options

A. `151`
B. `121`
C. `141`
D. `111`

Explanation

To find the least number which when divided by 12, 16, 24, and 36 leaves a remainder of 7 in each case, we can follow these steps:

### Step 1: Find the LCM of the numbers
First, we need to find the least common multiple (LCM) of the numbers 12, 16, 24, and 36.

1. **Prime Factorization**:
- 12 = 2^2 × 3^1
- 16 = 2^4
- 24 = 2^3 × 3^1
- 36 = 2^2 × 3^2

2. **Identify the highest powers of all prime factors**:
- For 2, the highest power is 2^4 (from 16).
- For 3, the highest power is 3^2 (from 36).

3. **Calculate the LCM**:
LCM = 2^4 × 3^2 = 16 × 9 = 144.

### Step 2: Add the remainder to the LCM
Since we want a number that leaves a remainder of 7 when divided by these numbers, we will add 7 to the LCM.

- Required number = LCM + 7 = 144 + 7 = 151.

### Conclusion
The least number which when divided by 12, 16, 24, and 36 leaves a remainder of 7 is **151**.

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