Question

find the largest four digit number which when reduced by 54 is perfectly divisible by all even natural numbers less than 20

Answer 1

To Find :- the largest four digit number which when reduced by 54 is perfectly divisible by all even natural numbers less than 20 ?

Solution :-

→ Even natural numbers less than 20 are = 2, 4, 6, 8, 10, 12, 14, 16 and 18.

Now, to find the number divisible by all , we need to find the LCM of given even numbers.

LCM of 2, 4, 6, 8, 10, 12, 14, 16 and 18 :-

2 | 2 - 4 - 6 - 8 - 10 - 12 - 14 - 16 - 18

2 | 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9

2 | 1 - 1 - 3 - 2 - 5 - 3 - 7 - 4 - 9

3 | 1 - 1 - 3 - 1 - 5 - 3 - 7 - 2 - 9

| 1 - 1 - 1 - 1 - 5 - 1 - 7 - 2 - 3

LCM = 2 * 2 * 2 * 3 * 5 * 7 * 2 * 3 = 5040 .

Now, Largest Four digits divided by all given even numbers is = 5040 .

Therefore,

→ The largest four digit number which when reduced by 54 is perfectly divisible by all given even natural numbers is = 5040 + 54 = 5094 (Ans.)

Learn More :-

Find the least number which when divide by 626, 618 and 676 leaves a remainder 3 in each

case.

https://brainly.in/question/23444967

find the smallest perfect square number that is divisible by 6 ,7 ,8 and 27

https://brainly.in/question/23226397