Which of the following represents the largest 4 digit number which can be added to 7855 in order to make the derived number divisible by each of the following numbers: 12, 14, 21, 33 and 54?
Answers
Answer:
Explanation:
Four digit number = 7855 ( Given)
The smallest number that is divisible by 12 (=2x2x3),
The smallest number that is divisible by 14 (=2x7),
The smallest number that is divisible by 21 (=3x7),
The smallest number that is divisible by 33 (=3x11), and
The smallest number that is divisible by 54 (=3x3x3x2)
The numbers are the least common multiple of the said numbers, which means that it has the minimum number of factors in the said numbers allowing them to be divisible by each of them.
Thus,
LCM is 2 x 2 x 3 x 3 x 3 x 7 x 11 = 8316.
So, 8316 - 7855
= 461
Therefore, 461 needs to added to 7355 so that it is divisible by the given 5 numbers. But we want a four digit number that should be multiple of 8316.
= 8316 ×2 = 16632.
= 16632 - 7855
= 8777
Answer:
Explanation:
Four digit number = 7855 ( Given)
The smallest number that is divisible by 12 (=2x2x3),
The smallest number that is divisible by 14 (=2x7),
The smallest number that is divisible by 21 (=3x7),
The smallest number that is divisible by 33 (=3x11), and
The smallest number that is divisible by 54 (=3x3x3x2)
The numbers are the least common multiple of the said numbers, which means that it has the minimum number of factors in the said numbers allowing them to be divisible by each of them.
Thus,
LCM is 2 x 2 x 3 x 3 x 3 x 7 x 11 = 8316.
So, 8316 - 7855
= 461
Therefore, 461 needs to added to 7355 so that it is divisible by the given 5 numbers. But we want a four digit number that should be multiple of 8316.
= 8316 ×2 = 16632.
= 16632 - 7855
= 8777