Find the smallest number which when divided by 18, 12, and 24 leaves a remainder of 16, 10, and 22 respectively.
ʏᴇ ᴍᴇʀᴇᴋᴏ ᴍᴀʀ ᴋᴇ ʜɪ ᴍᴀɴᴇɢɪ
Answers
Answer:
70
Explanation: A number when divided by divisors 18,12,24 should leave a remainder's 16,10 and 22 respectively.
When you see the divisors and the remainders, the remainders are exactly 2 less than the divisors.
The easiest of doing this problem is find out the LCM of the three numbers and reduce it by 2. That will be the smallest number as required by the question. The LCM will be divisible by all the three numbers and when you reduce 2 from the LCM the remainder will be two less than the divisors.
The LCM for three numbers 18, 12 and 24 is 72 . when you reduce 2 from LCM 72 you will get the answer as 70.
The difference between 18, 12, 24 and 16, 10, 22 respectively is 2. So the number which when divided by these numbers to get the latter numbers is 70. So that this number is 2 numbers away from being completely divisible in each case and leaves remainders 16, 10, 22 respectively.