How many numbers are there from 11 to 131 which are divisible by both 5 and 7?

Options

A. a. 4
B. b. 3
C. c. 2
D. d. 5

Answer

To solve the problem of how many numbers from 11 to 131 are divisible by both 5 and 7, we can follow these steps:

### Step 1: Find the Least Common Multiple (LCM)
To find numbers that are divisible by both 5 and 7, we first need to calculate their least common multiple (LCM).

The LCM of 5 and 7 is:
\[ \text{LCM}(5, 7) = 5 \times 7 = 35 \]

### Step 2: Determine the Range
We need to find numbers between 11 and 131 that are divisible by 35.

### Step 3: Find the First Multiple of 35
To find the first multiple of 35 that is greater than or equal to 11, we can calculate:
- The first multiple of 35 is 35 itself.

### Step 4: Find the Last Multiple of 35
Next, we need to find the largest multiple of 35 that is less than or equal to 131.
- The multiples of 35 are: 35, 70, 105, 140...
- The largest multiple of 35 that is less than or equal to 131 is 105.

### Step 5: List the Multiples of 35
Now we can list the multiples of 35 between 11 and 131:
- 35
- 70
- 105

### Step 6: Count the Multiples
Now, we count the multiples we found:
- There are 3 multiples of 35 between 11 and 131: 35, 70, and 105.

### Conclusion
Thus, the total number of numbers from 11 to 131 that are divisible by both 5 and 7 is:
\[ \text{Answer} = 3 \]

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