Four bells begin to ring together and ring respectively at an interval of 50 secs, 40 secs, 60 secs and 70 secs. After how much time will they again ring together?

Options

A. 90mins
B. 70 mins
C. 100 mins
D. 60 mins

Answer

To find out after how much time the four bells will ring together again, we need to calculate the Least Common Multiple (LCM) of their ringing intervals: 50 seconds, 40 seconds, 60 seconds, and 70 seconds.

### Step-by-Step Solution:

**Step 1: List the ringing intervals.**
- The intervals are: 50 seconds, 40 seconds, 60 seconds, and 70 seconds.

**Step 2: Prime factorization of each interval.**
- 50 = 2 × 5²
- 40 = 2³ × 5
- 60 = 2² × 3 × 5
- 70 = 2 × 5 × 7

**Step 3: Identify the highest power of each prime factor.**
- For the prime factor 2: the highest power is 2³ (from 40).
- For the prime factor 3: the highest power is 3¹ (from 60).
- For the prime factor 5: the highest power is 5² (from 50).
- For the prime factor 7: the highest power is 7¹ (from 70).

**Step 4: Calculate the LCM using the highest powers.**
- LCM = 2³ × 3¹ × 5² × 7¹
- LCM = 8 × 3 × 25 × 7

**Step 5: Calculate step by step.**
1. Calculate 8 × 3 = 24
2. Calculate 24 × 25 = 600
3. Calculate 600 × 7 = 4200

So, the LCM of 50, 40, 60, and 70 is 4200 seconds.

**Step 6: Convert seconds into minutes.**
- To convert seconds into minutes, divide by 60.
- 4200 seconds ÷ 60 = 70 minutes.

### Final Answer:
The four bells will ring together again after **70 minutes**.

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