Question

Find the least five digit number which leaves remainder 3 in each case when divided by 5 10 12 15 18 25 and 30

Answer 1

$Find\ the\ LCM\ of\ the\ required\ numbers. \\ \\ 5\ |\underline{5, 10, 12, 15, 18, 25, 30} \\ 2\ |\underline{1, 2, 12, 3, 18, 5, 6} \\ 3\ |\underline{1, 1, 6, 3, 9, 5, 3} \\ 1\ |\underline{1, 1, 2, 1, 3, 5, 1} \\ \\ LCM = 5 \times 2 \times 3 \times 2 \times 3 \times 5 = 900 \\ \\ \\ Then\ find\ the\ least\ 5\ digit\ multiple\ of\ 900. \\ \\ Least\ 5\ digit\ number\ is\ 10000. \\ \\ 10000\ divided\ by\ 900\ leaves\ quotient\ 11.$

$\\ \\ \therefore (11 + 1)900 = 12 \times 900 = 10800\ is\ the\ least\ 5\ digit\ multiple\ of\ 900. \\ \\ Add\ the\ remainder\ 3\ mentioned\ in\ the\ question. \\ \\ 10800 + 3 = 10803 \\ \\ \therefore 10803\ is\ the\ answer. \\ \\ Hope\ this\ may\ be\ helpful. \\ \\ Please\ mark\ my\ answer\ as\ the\ \bold{brainliest}\ if\ this\ may\ be\ helpful. \\ \\ Thank\ you.\ Have\ a\ nice\ day.$

Answer 2

Thanks very muchbs nnd nnendmemmd sm.nsjd nnmemd nenemememekem e