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Find the smallest number of 4 digits which is exactly divisible by 12, 15, 21 and 30.
- a)1580
- b)1420
- c)1260
- d)1056
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Find the smallest number of 4 digits which is exactly divisible by 12,...
Least 4 digit number = 1000
LCM of (12, 15, 21, 30) = 420
On dividing 420 by 1000, leaves remainder = 160
So answer = 1000 + (420 – 160)
LCM of (12, 15, 21, 30) = 420
On dividing 420 by 1000, leaves remainder = 160
So answer = 1000 + (420 – 160)
Most Upvoted Answer
Find the smallest number of 4 digits which is exactly divisible by 12,...
To find the smallest number of 4 digits which is exactly divisible by 12, 15, 21, and 30, we need to find the least common multiple (LCM) of these numbers.
Finding the LCM involves finding the smallest number that is divisible by all the given numbers. We can find the LCM by prime factorizing each number and taking the highest powers of all the prime factors.
Prime factorization of 12:
12 = 2^2 * 3
Prime factorization of 15:
15 = 3 * 5
Prime factorization of 21:
21 = 3 * 7
Prime factorization of 30:
30 = 2 * 3 * 5
Now, we need to take the highest powers of all the prime factors:
2^2 * 3 * 5 * 7 = 420
So, the LCM of 12, 15, 21, and 30 is 420.
Since we need to find the smallest number of 4 digits, we need to find the smallest multiple of 420 that has 4 digits.
The smallest multiple of 420 that has 4 digits is obtained by multiplying 420 by 3:
420 * 3 = 1260
Therefore, the smallest number of 4 digits which is exactly divisible by 12, 15, 21, and 30 is 1260.
Hence, the correct answer is option C) 1260.
Finding the LCM involves finding the smallest number that is divisible by all the given numbers. We can find the LCM by prime factorizing each number and taking the highest powers of all the prime factors.
Prime factorization of 12:
12 = 2^2 * 3
Prime factorization of 15:
15 = 3 * 5
Prime factorization of 21:
21 = 3 * 7
Prime factorization of 30:
30 = 2 * 3 * 5
Now, we need to take the highest powers of all the prime factors:
2^2 * 3 * 5 * 7 = 420
So, the LCM of 12, 15, 21, and 30 is 420.
Since we need to find the smallest number of 4 digits, we need to find the smallest multiple of 420 that has 4 digits.
The smallest multiple of 420 that has 4 digits is obtained by multiplying 420 by 3:
420 * 3 = 1260
Therefore, the smallest number of 4 digits which is exactly divisible by 12, 15, 21, and 30 is 1260.
Hence, the correct answer is option C) 1260.
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Community Answer
Find the smallest number of 4 digits which is exactly divisible by 12,...
Least 4 digit number = 1000
LCM of (12, 15, 21, 30) = 420
On dividing 420 by 1000, leaves remainder = 160
So answer = 1000 + (420 – 160)
LCM of (12, 15, 21, 30) = 420
On dividing 420 by 1000, leaves remainder = 160
So answer = 1000 + (420 – 160)
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Find the smallest number of 4 digits which is exactly divisible by 12, 15, 21 and 30.a)1580b)1420c)1260d)1056e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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