Question

What are the largest four digit nymber and smallest three digit number divisible by 6, 15, 21, 24?

Answer 1

Answer:

Step-by-step explanation:

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6 = 2 × 3

15 = 5 × 3

21 = 7 × 3

24 = 2 × 2 × 2 × 3

So, lcm = 2 × 2 × 2 × 3 × 5 × 7 = 840.

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The largest number in 4 digits = 9999

Now, 9999 = (840 × 11) + 759

So, remainder is = 759

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

= 9999 - 759

= 9240.

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

= lcm of 6, 15, 21 and 24

= 840

Answer 2

6 = 2*3

15 = 3*5

21 = 3*7

24 = 2³*3

∴ LCM of 6 , 15 , 21 , 24 =  2³ * 3 * 5 * 7 = 840

.

largest four digit number = 9999

9999/840   ->  Quotient = 11  

Remainder = 759

.

therefore , largest 4 digit number divisible by 6, 15, 21, 24 = 9240

..

LCM = 840

since , 840 is a three digit number and it is their LCM (Least Common Multiple) ...

Therefore, smallest three digit number divisible by 6, 15, 21, 24 = 840

.

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