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Find the smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.
- a)1239
- b)1241
- c)1243
- d)1245
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the smallest possible number which on adding 19 becomes exactly d...
Solution:
45 x 28 = 1, 260
36 x 35 = 1, 260
28 x 45 = 1, 260
Least Common Multiple (LCM) of 28, 36, and 45 is 1, 260
So, 1, 260 subtracted by 19 (smallest number which on adding 19)
will be 1, 241
Answer: 1, 241
LCM or the Least Common Multiple is the terminology for the common or similar multiple/s of more than one numbers.
Most Upvoted Answer
Find the smallest possible number which on adding 19 becomes exactly d...
To find the smallest possible number that is divisible by 28, 36, and 45, we need to find the least common multiple (LCM) of these three numbers.
Step 1: Find the prime factors of each number.
- Prime factors of 28: 2, 2, 7 (2 x 2 x 7)
- Prime factors of 36: 2, 2, 3, 3 (2 x 2 x 3 x 3)
- Prime factors of 45: 3, 3, 5 (3 x 3 x 5)
Step 2: Identify the largest exponent for each prime factor.
- Largest exponent of 2: 2 (from 2 x 2)
- Largest exponent of 3: 3 (from 3 x 3)
- Largest exponent of 7: 1 (from 7)
- Largest exponent of 5: 1 (from 5)
Step 3: Multiply the prime factors with their largest exponents.
2^2 x 3^3 x 7^1 x 5^1 = 4 x 27 x 7 x 5 = 3780
Step 4: Add 19 to the result.
3780 + 19 = 3799
Hence, the smallest possible number that on adding 19 becomes exactly divisible by 28, 36, and 45 is 3799.
Therefore, option B (1241) is incorrect.
Step 1: Find the prime factors of each number.
- Prime factors of 28: 2, 2, 7 (2 x 2 x 7)
- Prime factors of 36: 2, 2, 3, 3 (2 x 2 x 3 x 3)
- Prime factors of 45: 3, 3, 5 (3 x 3 x 5)
Step 2: Identify the largest exponent for each prime factor.
- Largest exponent of 2: 2 (from 2 x 2)
- Largest exponent of 3: 3 (from 3 x 3)
- Largest exponent of 7: 1 (from 7)
- Largest exponent of 5: 1 (from 5)
Step 3: Multiply the prime factors with their largest exponents.
2^2 x 3^3 x 7^1 x 5^1 = 4 x 27 x 7 x 5 = 3780
Step 4: Add 19 to the result.
3780 + 19 = 3799
Hence, the smallest possible number that on adding 19 becomes exactly divisible by 28, 36, and 45 is 3799.
Therefore, option B (1241) is incorrect.
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Find the smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.a)1239b)1241c)1243d)1245Correct answer is option 'B'. 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 smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.a)1239b)1241c)1243d)1245Correct answer is option 'B'. 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 smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.a)1239b)1241c)1243d)1245Correct answer is option 'B'. Can you explain this answer?.
Find the smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.a)1239b)1241c)1243d)1245Correct answer is option 'B'. 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 smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.a)1239b)1241c)1243d)1245Correct answer is option 'B'. 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 smallest possible number which on adding 19 becomes exactly divisible by 28, 36 and 45.a)1239b)1241c)1243d)1245Correct answer is option 'B'. Can you explain this answer?.
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