Question

. Tom has 72 inches of copper wire and 42 inches of steel wire. What is the largest piece of wire
he can cut so that each piece is the same?
1. Find the greatest number of four digits which is exactly divisible by each of 12, 18, 40 and 45.
TP11 -​

Answer 1

Answer:

1). Length of the largest piece of wire is 6 inches.

2). Required largest 4-Digit number is 9900.

Step-by-step explanation:

1).

Given:

length of copper wire = 72 inches

length of steel wire = 42 inches.

To find: Length of the largest piece of wire that is cut so that all piece are equal.

To find the require number we find the HCF of 72 and 42

72 = 2 × 2 × 2 × 3 × 3

42 = 2 × 3 × 7

HCF = 2 × 3 = 6

Therefore, Length of the largest piece of wire is 6 inches.

2).

Given Numbers 12 , 18 , 40 , 45.

To find: Largest 4 digit number number exactly divisible by given numbers.

To find the required number first we find the LCM of given numbers.

12 = 2 × 2 × 3

18 = 2 × 3 × 3

40 = 2 × 2 × 5

45 = 3 × 3 × 5

LCM = 2 × 3 × 2 × 3 × 5 = 180

Now we divide the greatest 4 digit number with the obtained LCM.

Greatest  4-Digit number = 9999

On division 9999 by 180. we get,

Quotient = 55

Remiander = 99

So, the Required 4-Digit number = 9999 - 99 = 9900.

Therefore, Required largest 4-Digit number is 9900.