Question

The traffic lights at three different road crossings change after every
seconds and 108 seconds. If they start changing simultaneously at 8 a.m., after how much
time will they change again simultaneously?
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Answer 1

ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴛʀᴀғғɪᴄ ʟɪɢʜᴛ ᴀᴛ ᴛʜʀᴇᴇ ᴅɪғғᴇʀᴇɴᴛ ʀᴏᴀᴅ ᴄʀᴏssɪɴɢ ᴄʜᴀɴɢᴇ ᴀғᴛᴇʀ ᴇᴠᴇʀʏ 48 sᴇᴄᴏɴᴅs,72 sᴇᴄᴏɴᴅs ᴀɴᴅ 108 sᴇᴄᴏɴᴅs ʀᴇsᴘᴇᴄᴛɪᴠᴇʟʏ. ʜᴇɴᴄᴇ,ᴀғᴛᴇʀ 7 ᴍɪɴ ᴀɴᴅ 12 sᴇᴄᴏɴᴅs ᴛʜᴇʏ ᴡɪʟʟ ʙʟɪɴᴋ sɪᴍᴜʟᴛᴀɴᴇᴏᴜsʟʏ.

Answer 2

Answer:

Given that traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.

So let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds

48 = 2 × 2 × 2 × 2 × 3

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

Hence LCM of 48, 72 and 108 is (2 × 2 × 2 × 2 × 3 × 3 × 3) = 432

So after 432 seconds they will change simultaneously

We know that 60 seconds = 1 minute

so on dividing 432 / 60 we get 7 as quotient and 12 as reminder

Hence, 432 seconds = 7 min 12 seconds

Therefore the time is = 7 a.m. + 7 minutes 12 seconds

Hence the lights change simultaneously at = 7:07:12 a.m