Question

The greatest 4-digit number exactly divisible
by 8, 10 and 12 is​

Answer 1

Answer:

2 is the answer

Step-by-step explanation:

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Answer 2

Answer:

9960 is the greatest 4 digit number divisible by 8, 10, and 12.

Step-by-step explanation:

Let the number be x

So, firstly we can say that,

1000 < x < 9999

Now, we know that,

x must be divisible by 8, 10 and 12, then that number must be a common multiple of 8, 10, and 12.

Hence, we take their LCM,

LCM (8, 10, 12) = 120

Now, remember I said 1000 < x < 9999, this is because neither 1000 nor 9999 is a multiple of 120, that is why I said that.

So, the 1st common multiple is 120.

2nd common multiple will be 120 × 2 = 240

3rd common multiple will be 120 × 3 = 360

.

.

.

and so on.

Now, this number is between 1000 and 9999

To find that number, we can either do it by trial and error, or divide 9999 by 120 and find the Quotient, this is because 9999 is the greatest 4 digit number.

9999 ÷ 120 = (Q = 83) and (R = 39)

Thus,

83rd common multiple is the largest 4 digit number divisible by 8, 10, and 12, as the Quotient is 83, with a remainder.

Thus,

x = 120 × 83

x = 9960

Hence,

9960 is the greatest 4 digit number divisible by 8, 10, and 12.

we can check this,

1000 < 9960 < 9999

also,

9960 ÷ 8 = 1245

9960 ÷ 10 = 996

9960 ÷ 12 = 830

So, it is true

Hope it helped and believing you understood it........All the best