Question

=
3
30
х
245 7
15
.: The other number is
49
EXERCISE (1
1. Find the least number which when divided by 16, 18, 24 leaves the remainder 4,
but there is no remainder when it devided by 7.
2. Find the least number from which 11 must he suhtronted to​

Answer 1

Answer:

okyy it's 4 and second answer is 5

Answer 2

Answer:

1. Find the least number which when divided by 16, 18, 24 leaves the remainder 4, but there is no remainder when it devided by 7.

Ans) First of all we have to take the L.C.M. of 16, 18 and 20

Prime factorization of 16 = 2*2*2*2

Prime factorization of 18 = 2*3*3

Prime factorization = 20 = 2*2*5

= 2*2*2*2*3*3*5

L.C.M. of 16, 18 and 20 = 720

Now, the L.C.M. of 16, 18 and 20 is 720.

So, the required number will be in the form of (720*x) + 4

Now, we have to apply the hit and trial method to find the least value of x for  

which (720*x)+ 4 is divisible by 7 ... by putting x = 1, 2, 3, 4..n.

First by putting x = 1

⇒ (720*1) + 4

⇒ 720 + 4

⇒ 724

724 is not divisible by 7.

Now, putting x = 2

⇒ (720*2) + 4

⇒ 1440 + 4

⇒ 1444

1444 is also not divisible by 7.

Now, putting x = 3

⇒ (720*3) + 4

⇒ 2160 + 4

⇒ 2164

2164 is also not divisible by 7

Now, putting x = 4

⇒ (720*4) + 4

⇒ 2880 + 4

⇒ 2884

2884 is exactly divisible by 7

So, for the value of x = 4, the required number comes 2884.  

2884 is the least number which when divided by 16, 18 and 20 leaves a

remainder 4 in each case but exactly divisible by 7.

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