Question

find the least multiple of 7 which leaves a reminder of 4 when divided by 6,9,15 and 18.​

Answer 1

multiple of 7 leaves a remainder 4

ie 7x + 4

this should be equal to the LCM of 6, 9, 15, 18

finding LCM of 6, 9, 15, 18

we get 270

therefore 7x + 4 = 270

$7x + 4 = 270 \\ 7x = 270 - 4 \\ 7x = 266 \\ x = \frac{266}{7} \\ x = 38$

38 is the least multiple of 7 which leaves the remainder 4