Question

find the least number which when divided by 15,21,35,42 leaving remainder 7​

Answer 1

Find the least number which when divided by 15, 27, 35 and 42 leaves a remainder of 5 in each case. Let us see the factors of the 4 numbers.

15 = 3 x 5

27 = 3 x 3 x 3

35 = 5 x 7

42 = 2 x 3 x 7

The LCM of the four numbers is: 2 x 3 x 3 x 3 x 5 x 7 = 1890.

Next add 5 to the number: 1890 + 5 = 1895, which is your answer.

Check: 1895/15 = 126 + 5 remainder

1895/27 = 70 + 5 remainder

1895/35 = 54 + 5 remainder

1895/42 = 45 + 5 remainder