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What least possible 4-digit number, when divided by 12, 16, 18 and 20 leaves 21 as remainder?
- a)36
- b)133
- c)144
- d)1461
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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What least possible 4-digit number, when divided by 12, 16, 18 and 20 ...
Here least possible 4 digit number is needed that means we need the LCM We must first find LCM of 12, 16, 18 and 20 .
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What least possible 4-digit number, when divided by 12, 16, 18 and 20 ...
Finding the Least Possible 4-Digit Number with Remainder 21 When Divided by 12, 16, 18, and 20
To find the least possible 4-digit number that leaves a remainder of 21 when divided by 12, 16, 18, and 20, we need to find the smallest common multiple of these four numbers and add 21 to it.
Step 1: Find the prime factorization of each number.
12 = 2^2 x 3
16 = 2^4
18 = 2 x 3^2
20 = 2^2 x 5
Step 2: Write the prime factors with the highest exponent for each factor.
12 = 2^2 x 3^1 x 5^0
16 = 2^4 x 3^0 x 5^0
18 = 2^1 x 3^2 x 5^0
20 = 2^2 x 3^0 x 5^1
Step 3: Write the LCM by taking the highest exponent for each factor.
LCM = 2^4 x 3^2 x 5^1 = 720
Step 4: Add 21 to the LCM.
720 + 21 = 741
Therefore, the least possible 4-digit number that leaves a remainder of 21 when divided by 12, 16, 18, and 20 is 741.
The correct answer is option D.
To find the least possible 4-digit number that leaves a remainder of 21 when divided by 12, 16, 18, and 20, we need to find the smallest common multiple of these four numbers and add 21 to it.
Step 1: Find the prime factorization of each number.
12 = 2^2 x 3
16 = 2^4
18 = 2 x 3^2
20 = 2^2 x 5
Step 2: Write the prime factors with the highest exponent for each factor.
12 = 2^2 x 3^1 x 5^0
16 = 2^4 x 3^0 x 5^0
18 = 2^1 x 3^2 x 5^0
20 = 2^2 x 3^0 x 5^1
Step 3: Write the LCM by taking the highest exponent for each factor.
LCM = 2^4 x 3^2 x 5^1 = 720
Step 4: Add 21 to the LCM.
720 + 21 = 741
Therefore, the least possible 4-digit number that leaves a remainder of 21 when divided by 12, 16, 18, and 20 is 741.
The correct answer is option D.
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What least possible 4-digit number, when divided by 12, 16, 18 and 20 leaves 21 as remainder?a)36b)133c)144d)1461e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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