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The least number which when divided by 2, 3, 4, 5 and 6 leaves the remainder 1 in each case. If the same number is divided by 7 it leaves no remainder. The number is
- a)231
- b)301
- c)371
- d)441
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The least number which when divided by 2, 3, 4, 5 and 6 leaves the rem...
The least common multiple of 2, 3, 4, 5, 6 is their LCM=60.
So, the answer is the least number such that it is a multiple of 7 and a multiple of 60 leaving remainder 1.
∴The required answer is 301.
So, the answer is the least number such that it is a multiple of 7 and a multiple of 60 leaving remainder 1.
∴The required answer is 301.
Most Upvoted Answer
The least number which when divided by 2, 3, 4, 5 and 6 leaves the rem...
To find the least number that satisfies the given conditions, we need to find the least common multiple (LCM) of 2, 3, 4, 5, and 6.
Finding the LCM involves finding the product of the highest powers of all prime factors in the given numbers.
Prime factors of the given numbers:
- 2: 2
- 3: 3
- 4: 2^2
- 5: 5
- 6: 2 x 3
The LCM is found by taking the highest power of each prime factor:
LCM = 2^2 x 3 x 5 = 60
So, the least number that satisfies the given conditions is 60.
To check if this number leaves a remainder of 1 when divided by 2, 3, 4, 5, and 6, we can perform the divisions:
- 60 ÷ 2 = 30 with a remainder of 0 (not 1)
- 60 ÷ 3 = 20 with a remainder of 0 (not 1)
- 60 ÷ 4 = 15 with a remainder of 0 (not 1)
- 60 ÷ 5 = 12 with a remainder of 0 (not 1)
- 60 ÷ 6 = 10 with a remainder of 0 (not 1)
Since 60 does not satisfy the condition of leaving a remainder of 1 when divided by 2, 3, 4, 5, and 6, it is not the correct answer.
To find the correct answer, we need to add the LCM to itself until we find a number that satisfies the given conditions.
Let's check the next number, 60 + 60 = 120:
- 120 ÷ 2 = 60 with a remainder of 0 (not 1)
- 120 ÷ 3 = 40 with a remainder of 0 (not 1)
- 120 ÷ 4 = 30 with a remainder of 0 (not 1)
- 120 ÷ 5 = 24 with a remainder of 0 (not 1)
- 120 ÷ 6 = 20 with a remainder of 0 (not 1)
120 also does not satisfy the condition.
Let's continue adding the LCM to find the correct answer:
- 120 + 60 = 180:
- 180 ÷ 2 = 90 with a remainder of 0 (not 1)
- 180 ÷ 3 = 60 with a remainder of 0 (not 1)
- 180 ÷ 4 = 45 with a remainder of 0 (not 1)
- 180 ÷ 5 = 36 with a remainder of 0 (not 1)
- 180 ÷ 6 = 30 with a remainder of 0 (not 1)
180 does not satisfy the condition.
Let's add the LCM again:
- 180 + 60 = 240:
- 240 ÷ 2 = 120 with a remainder of 0 (not 1)
- 240 ÷ 3 = 80 with a remainder of 0 (not 1)
- 240
Finding the LCM involves finding the product of the highest powers of all prime factors in the given numbers.
Prime factors of the given numbers:
- 2: 2
- 3: 3
- 4: 2^2
- 5: 5
- 6: 2 x 3
The LCM is found by taking the highest power of each prime factor:
LCM = 2^2 x 3 x 5 = 60
So, the least number that satisfies the given conditions is 60.
To check if this number leaves a remainder of 1 when divided by 2, 3, 4, 5, and 6, we can perform the divisions:
- 60 ÷ 2 = 30 with a remainder of 0 (not 1)
- 60 ÷ 3 = 20 with a remainder of 0 (not 1)
- 60 ÷ 4 = 15 with a remainder of 0 (not 1)
- 60 ÷ 5 = 12 with a remainder of 0 (not 1)
- 60 ÷ 6 = 10 with a remainder of 0 (not 1)
Since 60 does not satisfy the condition of leaving a remainder of 1 when divided by 2, 3, 4, 5, and 6, it is not the correct answer.
To find the correct answer, we need to add the LCM to itself until we find a number that satisfies the given conditions.
Let's check the next number, 60 + 60 = 120:
- 120 ÷ 2 = 60 with a remainder of 0 (not 1)
- 120 ÷ 3 = 40 with a remainder of 0 (not 1)
- 120 ÷ 4 = 30 with a remainder of 0 (not 1)
- 120 ÷ 5 = 24 with a remainder of 0 (not 1)
- 120 ÷ 6 = 20 with a remainder of 0 (not 1)
120 also does not satisfy the condition.
Let's continue adding the LCM to find the correct answer:
- 120 + 60 = 180:
- 180 ÷ 2 = 90 with a remainder of 0 (not 1)
- 180 ÷ 3 = 60 with a remainder of 0 (not 1)
- 180 ÷ 4 = 45 with a remainder of 0 (not 1)
- 180 ÷ 5 = 36 with a remainder of 0 (not 1)
- 180 ÷ 6 = 30 with a remainder of 0 (not 1)
180 does not satisfy the condition.
Let's add the LCM again:
- 180 + 60 = 240:
- 240 ÷ 2 = 120 with a remainder of 0 (not 1)
- 240 ÷ 3 = 80 with a remainder of 0 (not 1)
- 240
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The least number which when divided by 2, 3, 4, 5 and 6 leaves the rem...
Answer is B (301)
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The least number which when divided by 2, 3, 4, 5 and 6 leaves the remainder 1 in each case. If the same number is divided by 7 it leaves no remainder. The number isa)231b)301c)371d)441Correct answer is option 'B'. Can you explain this answer?
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