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What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
- a)1012
- b)1022
- c)1122
- d)1222
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
What is the least four-digit number when divided by 3, 4, 5 and 6 leav...
The lowest 4-digit number is 1000.
LCM of 3, 4, and 5 is 60.
Dividing 1000 by 60, we get the remainder 40. Thus, the lowest 4-digit number that exactly divisible by 3, 4, and 5 is 1000 + (60 - 40) = 1020.
Now, add the remainder 2 that's required. Thus, the answer is 1022.
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What is the least four-digit number when divided by 3, 4, 5 and 6 leav...
Given: A four-digit number that leaves a remainder of 2 when divided by 3, 4, 5, and 6.
To find: The least four-digit number that satisfies the given condition.
Solution:
We need to find a number that leaves a remainder of 2 when divided by 3, 4, 5, and 6. This means that the number should be of the form:
N = LCM(3, 4, 5, 6) x K + 2
where K is an integer and LCM is the Least Common Multiple of 3, 4, 5, and 6.
LCM (3, 4, 5, 6) = 60
So, N = 60K + 2
We need to find the least four-digit number of this form.
The smallest value of K that gives a four-digit number is K = 17.
Substituting K = 17 in the above equation, we get:
N = 60 x 17 + 2 = 1022
Therefore, the least four-digit number that leaves a remainder of 2 when divided by 3, 4, 5, and 6 is 1022.
Answer: Option (b) 1022.
To find: The least four-digit number that satisfies the given condition.
Solution:
We need to find a number that leaves a remainder of 2 when divided by 3, 4, 5, and 6. This means that the number should be of the form:
N = LCM(3, 4, 5, 6) x K + 2
where K is an integer and LCM is the Least Common Multiple of 3, 4, 5, and 6.
LCM (3, 4, 5, 6) = 60
So, N = 60K + 2
We need to find the least four-digit number of this form.
The smallest value of K that gives a four-digit number is K = 17.
Substituting K = 17 in the above equation, we get:
N = 60 x 17 + 2 = 1022
Therefore, the least four-digit number that leaves a remainder of 2 when divided by 3, 4, 5, and 6 is 1022.
Answer: Option (b) 1022.
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