Find the three-digit smallest number which when divided by 3, 5 or 7, the remainder 3 in each case ?
(1) 102 (2) 108 (3) 110 (4) 112
Answers
Answer:
108
Step-by-step explanation:
lcm of the nos. is 105
since remainder is 3in each case, we add 3 to the lcm
hence the no. is 108
Answer:
The correct answer is option(2) 108
Step-by-step explanation:
To find,
The three-digit smallest number which when divided 3,5, or 7 gives the remainder 3 in each case.
Recall the concept
LCM or Least common multiple :
The least common multiple of two more numbers is defined as the smallest number that divides the numbers evenly.
Solution:
The smallest number when divided by 3,5, and 7 is the LCM of the numbers 3,5,7
Since the numbers 3,5,7 are coprime. LCM of the numbers 3,5,7 = 3×5×7 = 105
To get the remainder '3' we should add three with the LCM = 105+3 = 108. which is a three-digit number
The three-digit smallest number which when divided 3,5, or 7 gives the remainder 3 in each case. = 108
∴ The correct answer is option(2) 108
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