Question
48. The smallest four-digit number that is a multiple of 6, 7 and 4 is:
(1) 1006
(2) 1008
(3) 1000
(4) 1002
Click To Show Answer
उत्तर : (2) 1008
कारण: First, find the Least Common Multiple (LCM) of 6, 7, and 4:
6 = 2 x 3
7 = 7
4 = 2 x 2
LCM(6, 7, 4) = 2 x 2 x 3 x 7 = 84
Now, the smallest four-digit number is 1000.
We need to find the smallest multiple of 84 that is greater than or equal to 1000.
Divide 1000 by 84: 1000 ÷ 84 ≈ 11.9
This means the 11th multiple of 84 will be less than 1000, and the 12th multiple will be greater than or equal to 1000.
84 x 12 = 1008
Therefore, the smallest four-digit number divisible by 6, 7, and 4 is 1008.
कारण: First, find the Least Common Multiple (LCM) of 6, 7, and 4:
6 = 2 x 3
7 = 7
4 = 2 x 2
LCM(6, 7, 4) = 2 x 2 x 3 x 7 = 84
Now, the smallest four-digit number is 1000.
We need to find the smallest multiple of 84 that is greater than or equal to 1000.
Divide 1000 by 84: 1000 ÷ 84 ≈ 11.9
This means the 11th multiple of 84 will be less than 1000, and the 12th multiple will be greater than or equal to 1000.
84 x 12 = 1008
Therefore, the smallest four-digit number divisible by 6, 7, and 4 is 1008.
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