Question

The greatest number of four digits which is divisible by each one of the numbers 12, 18, 21. and 28 is

Answer 1

Answer:

9828

Hope this helps!

Step-by-step explanation:

The numbers divisible by all of 12, 18, 21 and 28, are simply the multiples of the lcm of 12, 18, 21 and 28.  So start by finding their lcm.  This is easy from the prime factorizations:

12 = 2² 3¹

18 = 2¹ 3²

21 = 3¹ 7¹

28 = 2² 7¹

The lcm is then

m = 2² 3² 7¹  = 252.

So now the question is asking for the greatest number of four digits that is a multiple of 252.

Since 10000 / 252 ≈ 39.7,

we see that 39 × 252 is less than 10000 (so has 4 digits), while 40 × 252 is greater than 10000 (so has 5 digits).

So the number we want is

39 × 252 = 9828