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Find the least number which when divided by 10, 15, 18 and 30 leaves remainders 6, 11, 14 and 26 respectively.
- a)72
- b)86
- c)85
- d)90
- e)94
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the least number which when divided by 10, 15, 18 and 30 leaves r...
Since 10-6 = 4, 15-11 = 4, 18-14 = 4, 30-26 = 4
So answer will be the LCM of these numbers – 4
So 90 – 4
So answer will be the LCM of these numbers – 4
So 90 – 4
Most Upvoted Answer
Find the least number which when divided by 10, 15, 18 and 30 leaves r...
To find the least number that satisfies the given conditions, we can use the method of finding the least common multiple (LCM) of the given numbers.
The given numbers are 10, 15, 18, and 30.
Step 1: Prime Factorization
Find the prime factorization of each number:
10 = 2 × 5
15 = 3 × 5
18 = 2 × 3 × 3
30 = 2 × 3 × 5
Step 2: LCM
To find the LCM, take the highest power of each prime factor that appears in the prime factorization of any of the numbers.
The LCM is calculated as follows:
LCM = (2^1) × (3^2) × (5^1) = 2 × 9 × 5 = 90
Step 3: Checking the Remainders
Now, we can check if the number 90 satisfies the given conditions.
When divided by 10, the remainder should be 6.
90 ÷ 10 = 9 with a remainder of 0, which is not equal to 6.
When divided by 15, the remainder should be 11.
90 ÷ 15 = 6 with a remainder of 0, which is not equal to 11.
When divided by 18, the remainder should be 14.
90 ÷ 18 = 5 with a remainder of 0, which is not equal to 14.
When divided by 30, the remainder should be 26.
90 ÷ 30 = 3 with a remainder of 0, which is not equal to 26.
Since the number 90 does not satisfy any of the given conditions, it is not the correct answer.
Step 4: Finding the Correct Answer
To find the correct answer, we need to find the next multiple of the LCM that satisfies the given conditions.
Adding the LCM to the previous number, we get:
90 + 90 = 180
When divided by 10, the remainder is 6.
180 ÷ 10 = 18 with a remainder of 0, which is not equal to 6.
When divided by 15, the remainder is 11.
180 ÷ 15 = 12 with a remainder of 0, which is not equal to 11.
When divided by 18, the remainder is 14.
180 ÷ 18 = 10 with a remainder of 0, which is not equal to 14.
When divided by 30, the remainder is 26.
180 ÷ 30 = 6 with a remainder of 0, which is not equal to 26.
Continuing this process, we find that the next multiple of the LCM that satisfies the given conditions is 270.
When divided by 10, the remainder is 6.
270 ÷ 10 = 27 with a remainder of 0, which is not equal to 6.
When divided by 15, the remainder is 11.
270 ÷ 15 = 18 with a remainder of 0, which is not equal to 11.
When divided by 18, the remainder is 14.
270 ÷
The given numbers are 10, 15, 18, and 30.
Step 1: Prime Factorization
Find the prime factorization of each number:
10 = 2 × 5
15 = 3 × 5
18 = 2 × 3 × 3
30 = 2 × 3 × 5
Step 2: LCM
To find the LCM, take the highest power of each prime factor that appears in the prime factorization of any of the numbers.
The LCM is calculated as follows:
LCM = (2^1) × (3^2) × (5^1) = 2 × 9 × 5 = 90
Step 3: Checking the Remainders
Now, we can check if the number 90 satisfies the given conditions.
When divided by 10, the remainder should be 6.
90 ÷ 10 = 9 with a remainder of 0, which is not equal to 6.
When divided by 15, the remainder should be 11.
90 ÷ 15 = 6 with a remainder of 0, which is not equal to 11.
When divided by 18, the remainder should be 14.
90 ÷ 18 = 5 with a remainder of 0, which is not equal to 14.
When divided by 30, the remainder should be 26.
90 ÷ 30 = 3 with a remainder of 0, which is not equal to 26.
Since the number 90 does not satisfy any of the given conditions, it is not the correct answer.
Step 4: Finding the Correct Answer
To find the correct answer, we need to find the next multiple of the LCM that satisfies the given conditions.
Adding the LCM to the previous number, we get:
90 + 90 = 180
When divided by 10, the remainder is 6.
180 ÷ 10 = 18 with a remainder of 0, which is not equal to 6.
When divided by 15, the remainder is 11.
180 ÷ 15 = 12 with a remainder of 0, which is not equal to 11.
When divided by 18, the remainder is 14.
180 ÷ 18 = 10 with a remainder of 0, which is not equal to 14.
When divided by 30, the remainder is 26.
180 ÷ 30 = 6 with a remainder of 0, which is not equal to 26.
Continuing this process, we find that the next multiple of the LCM that satisfies the given conditions is 270.
When divided by 10, the remainder is 6.
270 ÷ 10 = 27 with a remainder of 0, which is not equal to 6.
When divided by 15, the remainder is 11.
270 ÷ 15 = 18 with a remainder of 0, which is not equal to 11.
When divided by 18, the remainder is 14.
270 ÷
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Find the least number which when divided by 10, 15, 18 and 30 leaves remainders 6, 11, 14 and 26 respectively.a)72b)86c)85d)90e)94Correct answer is option 'B'. Can you explain this answer?
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