Question

what is the smallest no. that when divided by 35 , 56 , 91 leaves remaider of 7 in each case.

Answer 1

What is the smallest no. that when divided by 35 , 56 , 91 leaves remaider of 7 in each case

so 

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

now remainder should be 7

=> 3640 +7

= 3647

hence 3647 is 

the smallest no. that when divided by 35 , 56 , 91 leaves remaider of 7 in each case.

:)

Answer 2

35 = 7*5
56 = 7*2³
91  = 7*13

LCM = 7*5*2³*13 = 3640

The required no. = 3640+7 = 3647