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N is the smallest number which when added to the 2000 makes the resulting number divisible by 12, 16, 18 and 21, Then the N is
- a)11
- b)7
- c)9
- d)16
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
N is the smallest number which when added to the 2000 makes the result...
LCM of 12, 16, 18, 21 = 1008
1008*2 = 2016
N = 16
1008*2 = 2016
N = 16
Most Upvoted Answer
N is the smallest number which when added to the 2000 makes the result...
Finding the Smallest Number that Satisfies Given Conditions
To solve this problem, we need to find the smallest number that when added to 2000, the resulting number is divisible by 12, 16, 18, and 21. We can use the LCM (Least Common Multiple) of these numbers to find such a number.
Step 1: Find the LCM of 12, 16, 18, and 21
To find the LCM of these numbers, we can list their prime factors and take the highest power of each factor.
12 = 2² × 3
16 = 2⁴
18 = 2 × 3²
21 = 3 × 7
The LCM is then the product of these factors with the highest power:
LCM = 2⁴ × 3² × 7 = 1008
Step 2: Find the Remainder when 2000 is divided by the LCM
We need to find the remainder when 2000 is divided by 1008, which we can do by dividing 2000 by 1008 and taking the remainder.
2000 ÷ 1008 = 1 remainder 992
So the remainder is 992.
Step 3: Find the Smallest Number that when Added to 2000 Gives a Multiple of 1008
To find the smallest number that when added to 2000 gives a multiple of 1008, we need to subtract the remainder (992) from the LCM (1008).
1008 - 992 = 16
Therefore, the smallest number that when added to 2000 gives a multiple of 12, 16, 18, and 21 is 16. Hence, the correct answer is option 'D'.
To solve this problem, we need to find the smallest number that when added to 2000, the resulting number is divisible by 12, 16, 18, and 21. We can use the LCM (Least Common Multiple) of these numbers to find such a number.
Step 1: Find the LCM of 12, 16, 18, and 21
To find the LCM of these numbers, we can list their prime factors and take the highest power of each factor.
12 = 2² × 3
16 = 2⁴
18 = 2 × 3²
21 = 3 × 7
The LCM is then the product of these factors with the highest power:
LCM = 2⁴ × 3² × 7 = 1008
Step 2: Find the Remainder when 2000 is divided by the LCM
We need to find the remainder when 2000 is divided by 1008, which we can do by dividing 2000 by 1008 and taking the remainder.
2000 ÷ 1008 = 1 remainder 992
So the remainder is 992.
Step 3: Find the Smallest Number that when Added to 2000 Gives a Multiple of 1008
To find the smallest number that when added to 2000 gives a multiple of 1008, we need to subtract the remainder (992) from the LCM (1008).
1008 - 992 = 16
Therefore, the smallest number that when added to 2000 gives a multiple of 12, 16, 18, and 21 is 16. Hence, the correct answer is option 'D'.
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Community Answer
N is the smallest number which when added to the 2000 makes the result...
LCM of 12, 16, 18, 21 = 1008
1008*2 = 2016
N = 16
1008*2 = 2016
N = 16
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N is the smallest number which when added to the 2000 makes the resulting number divisible by 12, 16, 18 and 21, Then the N isa)11b)7c)9d)16e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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