A number m is such that when it is divided by 30,36 and 45, the remainder is always 7.Find the smallest possible value of m

  187

Step-by-step explanation:

The desired number will be 7 more than the least common multiple (LCM) of 30, 36, and 45.

30 and 36 have a greatest common factor of 6, so their least common multiple will be 30×36/6 = 180. This is also a multiple of 45, so 180 is the LCM of all three numbers. Seven more than this is 187.

The smallest possible value of m is 187.

Comment on the answer

Actually, the answer could be m = 180n +7, where n is any integer. If negative values of n are allowed, there is no "smallest", as the numbers tend toward negative infinity. For n=0, m will be 7, which will give the specified remainders. The quotient in each case will be 0, which may not be what you want. The above answer assumes n > 0.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,