Question

7 members find gold coins if 7 members takes equal no.of gold coins it divides excatly,if 2,3,4,5,6 members takes the gold coins 1 coin will remain , how many coins are there?

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

__________________________

★ Given :

7 members find gold coins if 7 members takes equal no.of gold coins it divides excatly,if 2,3,4,5,6 members takes the gold coins 1 coin will remain.

__________________________

★ To Find :

We have to find that how many coins are there ?

__________________________

★ Solution :

As, there are 7 members and the when all take coins there 1 coin left.

So, we have to find the L.C.M of 2, 3, 4, 5, 6

→ 2 = 2 * 1

→ 3 = 3 * 1

→ 4 = 2 * 2

→ 5 = 5 * 1

→ 6 = 3 * 2

» L.C.M = 2 * 2 * 3 * 5

» L.C.M = 4 * 15

» L.C.M = 60

Now, A.T.Q

After this 1 coin will be left. So,

Total Number of coins = 60 + 1

Total Number of coins = 61

$\small{\star{\boxed{\sf{Total \: Number \: of \: coins = 61}}}}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$

$\setlength{\unitlength}{0.19 cm}}\begin{picture}(12,4)\thicklines\put(12,40){ \#\:STAY\:HOME }\put(11,35){ \#\:STAY\: SAFETY }\put(20,20){\circle{10}}\put(19.5,21){\line(-1,0){1.5}}\put(20.5,21){\line(1,0){1.5}}\put(18.8,20.3){\circle*{0.7}}\put(21.1,20.3){\circle*{0.7}}\put(20,20.4){\line(0,-1){1.4}}\put(20.7,18.4){\line(-1,0){1.57}}\put(18.6,16.56){\line(0,-1){2}}\put(21.4,16.56){\line(0,-1){2}}\put(19,14.55){\line(-1,0){5}}\put(21,14.55){\line(1,0){5}}\put(14,14.55){\line(0,-1){16}}\put(26,14.55){\line(0,-1){16}}\put(14,14.55){\line(-4,3){5}}\put(26,14.55){\line(4,3){5}}\put(14,11){\line(-4,3){7.5}}\put(26,11){\line(4,3){7.5}}\put(9,18.3){\line(0,1){8.3}}\put(31,18.3){\line(0,1){8.3}}\put(33.5,16.6){\line(0,1){10}}\put(6.5,16.6){\line(0,1){10}}\put(3.5,26.5){\line(1,0){33}}\put(3.5,26.5){\line(0,1){20}}\put(3.5,46.5){\line(1,0){33}}\put(36.5,26.5){\line(0,1){20}}\put(14,-0.6){\line(1,0){12}}\put(14,-1.5){\line(1,0){12}}\put(14.4,-1.6){\line(0,-1){18.5}}\put(25.6,-1.6){\line(0,-1){18.5}}\put(20,-1.6){\line(0,-1){3}}\put(20,-4.6){\line(-1,-6){2.6}}\put(20,-4.6){\line(1,-6){2.6}}\put(14.4,-20){\line(-5,-6){3}}\put(25.6,-20){\line(5,-6){3}}\put(17.3,-20){\line(0,-1){3.7}}\put(17.3,-20){\line(-1,0){3}}\put(17.3,-23.6){\line(-1,0){6}}\put(22.6,-20){\line(0,-1){3.7}}\put(22.6,-20){\line(1,0){3}}\put(22.6,-23.6){\line(1,0){6}}\end{picture}$

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\put(1,1.2){\line(1,0){6.5}}\end{picture}$