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Find the greatest 3-digit number which is divisible by 8, 10 and 12.
- a)840
- b)480
- c)960
- d)980
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)...
L.C.M of 8, 10, 12 = 2 x 2 x 2 x 3 x 5 = 120
We have to find the greatest 3 digit multiple of 120
It can be seen that 120 x 8 =960 and 120 x 9 =1080.
Hence, the greatest 3- digit number exactly divisible by 8 , 10 and 12 is 960
Most Upvoted Answer
Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)...
To find the greatest 3-digit number that is divisible by 8, 10, and 12, we need to find the least common multiple (LCM) of these three numbers.
Step 1: Find the prime factorization of each number
- The prime factorization of 8 is 2 x 2 x 2.
- The prime factorization of 10 is 2 x 5.
- The prime factorization of 12 is 2 x 2 x 3.
Step 2: Determine the highest power of each prime factor
- The highest power of 2 is 2 x 2 x 2 = 8.
- The highest power of 3 is 3.
- The highest power of 5 is 5.
Step 3: Multiply the highest powers of each prime factor
To find the LCM, we multiply the highest powers of each prime factor:
8 x 3 x 5 = 120.
The LCM of 8, 10, and 12 is 120. However, we need to find the greatest 3-digit number that is divisible by these numbers.
Step 4: Find the largest multiple of the LCM that is a 3-digit number
To find the greatest 3-digit number that is divisible by 120, we divide the largest 3-digit number (999) by 120 and find the quotient.
999 ÷ 120 = 8 remainder 39.
Since we are looking for a multiple of 120 that is a 3-digit number, we subtract the remainder from 999.
999 - 39 = 960.
Therefore, the greatest 3-digit number that is divisible by 8, 10, and 12 is 960 (option C).
Step 1: Find the prime factorization of each number
- The prime factorization of 8 is 2 x 2 x 2.
- The prime factorization of 10 is 2 x 5.
- The prime factorization of 12 is 2 x 2 x 3.
Step 2: Determine the highest power of each prime factor
- The highest power of 2 is 2 x 2 x 2 = 8.
- The highest power of 3 is 3.
- The highest power of 5 is 5.
Step 3: Multiply the highest powers of each prime factor
To find the LCM, we multiply the highest powers of each prime factor:
8 x 3 x 5 = 120.
The LCM of 8, 10, and 12 is 120. However, we need to find the greatest 3-digit number that is divisible by these numbers.
Step 4: Find the largest multiple of the LCM that is a 3-digit number
To find the greatest 3-digit number that is divisible by 120, we divide the largest 3-digit number (999) by 120 and find the quotient.
999 ÷ 120 = 8 remainder 39.
Since we are looking for a multiple of 120 that is a 3-digit number, we subtract the remainder from 999.
999 - 39 = 960.
Therefore, the greatest 3-digit number that is divisible by 8, 10, and 12 is 960 (option C).
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Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)840b)480c)960d)980Correct answer is option 'C'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)840b)480c)960d)980Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)840b)480c)960d)980Correct answer is option 'C'. Can you explain this answer?.
Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)840b)480c)960d)980Correct answer is option 'C'. Can you explain this answer? for Class 6 2025 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)840b)480c)960d)980Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 6 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the greatest 3-digit number which is divisible by 8, 10 and 12.a)840b)480c)960d)980Correct answer is option 'C'. Can you explain this answer?.
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