Question

Find the least multiple of 7 which leaves remainder 4 when divided by 6, 9, 15 and 18. [5 marks]

Answer 1

We know, 6 = 2$\times$ 3
9 = 3 $\times$ 3
15 = 3 $\times$ 5
18 = 2 $\times$ 3 $\times$ 3
LCM (6, 9, 15, 18) = 90 [1 mark]
All common multiples are of the form: 90 $\times$ #
To leave a remainder 4, it should be of the form: (90 $\times$ #) + 4
[1 mark]
For multiple of 7, (90 $\times$ #) + 4 should be divisible by 7.
By trail and error, we assign values to # to verify. [1 mark]

For # = 1, number = 94, which is not a multiple of 7.
For # = 2, number = 184, which is not a multiple of 7.
For # = 3, number = 274, which is not a multiple of 7.
For # = 4, number = 364, which is divisible by 7.
Therefore, # = 4 and the least multiple is 364. [2 marks]