A frog jumps 3 steps and a rabbit jumps 7 steps at a time starting from a place O. At which of the following steps, they both will be jumping together ?

Question

Accepted Answer

To determine at which step both the frog and the rabbit will jump together, we need to find the least common multiple (LCM) of the number of steps each animal jumps. The frog jumps 3 steps at a time, and the rabbit jumps 7 steps at a time. Therefore, we need to find the LCM of 3 and 7.

1. **Finding the LCM of 3 and 7:**
   - The prime factors of 3 are: 3
   - The prime factors of 7 are: 7
   - Since 3 and 7 are both prime numbers and have no common factors other than 1, the LCM is simply their product: $3 \times 7 = 21$.

2. **Checking the options:**
   - **Option 1: 343**
     - 343 is not divisible by 21. $343 \div 21 \approx 16.333$, which is not an integer.
   - **Option 2: 371**
     - 371 is not divisible by 21. $371 \div 21 \approx 17.666$, which is not an integer.
   - **Option 3: 378**
     - 378 is divisible by 21. $378 \div 21 = 18$, which is an integer. This means both the frog and the rabbit will land on step 378 together.
   - **Option 4: 354**
     - 354 is not divisible by 21. $354 \div 21 \approx 16.857$, which is not an integer.

3. **Conclusion:**
   - Option 3 (378) is the correct answer because it is the only option that is a multiple of the LCM of 3 and 7, which is 21. Therefore, both the frog and the rabbit will jump together at step 378.