हिंदी में जवाब दो: Two bells ring at intervals of 18 minutes and 24 minutes respectively. If they ring together at 9:00 a.m., at what time will they next ring together?

Step 1: Find the Least Common Multiple (LCM)

To find when the bells will ring together again, we need to find the least common multiple (LCM) of their individual ringing intervals. The LCM will represent the smallest amount of time after which both events will coincide.

Step 2: Prime Factorization of 18

First, we find the prime factorization of 18. This means expressing 18 as a product of its prime factors.

Step 3: Prime Factorization of 24

Next, we find the prime factorization of 24. This means expressing 24 as a product of its prime factors.

Step 4: Calculate the LCM

To find the LCM, we take the highest power of each prime factor present in the factorizations of both numbers. For 2, the highest power is $2^3$. For 3, the highest power is $3^2$. Multiplying these together gives us the LCM.

Step 5: Determine the next ringing time

The bells will ring together again after 72 minutes. We convert 72 minutes into hours and minutes (1 hour and 12 minutes) and add this to the starting time of 9:00 a.m. to find the next time they ring together.

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