What are the largest 4 digit and the smallest

Asked by admin @ 16/08/2021 in Math viewed by 322 People

What are the largest 4 digit and smallest 3 digit numbers divisible by 6,15,21 & 24

Answered by admin @ 16/08/2021

Answer:

The largest 4 digit number is 9240 and smallest 3 digit number is 840.

Step-by-step explanation:

To find : What are the largest 4 digit and smallest 3 digit numbers divisible by 6,15,21 & 24 ?

Solution :

First we find the LCM of the numbers 6,15,21 & 24

2 | 6 15 21 24

2 | 3 15 21 12

2 | 3 15 21 6

3 | 3 15 21 3

5 | 1 5 7 1

7 | 1 1 7 1

| 1 1 1 1

$LCM(6,15,21,24)=2\times 2\times 2\times 3\times 5\times 7$

$LCM(6,15,21,24)=840$

The largest number in 4 digits = 9999

Now, $9999 = (840\times 11) + 759$

Remainder = 759

So the largest number, divisible by 6, 15, 21 and 24 is

$n= 9999 - 759$

$n= 9240$

The smallest number in 3 digits, divisible by 6, 15, 21 and 24 is LCM.

i.e. n=840

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