Question

Find the least number when divided by35, 56 and 91 leave the same remainder 7 in each case

Answer 1

The smallest number which when divided by 35, 56 and 91 = LCM of 35, 56 and 91

35 = 5 x 7
56 = 2 x 2 x 2 x 7
91 = 7 x 13

LCM = 7 x 5 x 2 x 2 x 2 x 13 = 3640

The smallest number that when divided by 35, 56, 91 leaves a remainder 7 in each case = 3640 + 7 = 3647.

An alternate method:

Find the LCM of 35, 56 and 91. For that find the factors of

35 = 5x7

56 = 2x2x2x7

91 = 7x13

So the LCM = 2x2x2x7x5x13 = 3640.

The number you want is 3640+7 = 3647.

Check: 3647/35 = 104 + 7 as remainder.

3647/56 = 65 + 7 as remainder.

3647/91= 40 + 7 as remainder.

The answer is 3647.

Hope This Helps :)