Question

Find the least number which when divided by 12 16 24 and 30 leaves a remainder 4 in each case but it is completely divisible by 7

Answer 1

lets find lcm of 12 16 24 and 30

12 = 2×2×3

16= 2×2×2×2

24= 2×2×2×3

30= 2×3×5

lcm is = 240

now because number should be divisible by 7 so we have to multiply it by 7 and add 4 to fulfill remainder case.

so number is = 240*7+4

= 980+4= 984

Answer 2

Let the least number be “N”.

Now N when divided by 12, 16, 24 and 30 leaves remainder 4 in each case.

So, we can say (N-4) is completely divisible by 12, 16, 24 and 30.

Thus, (N−4)=LCM(12,16,24,30)

=>(N−4)=240

=>N = 244

But N should be completely divisible by 7. Thus, general form of N can be taken as:

N = 244k + 4

Now, for k = 4, N = 900 which is completely divisible by 7.