Question

a number that is divisible by 1,2,3,4,5,6,7,8,9 and 10

Answer 1

Step-by-step explanation:

lcm of 1 to 10 no.s = 10×9×8×7 = 5040

Answer 2

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➺Informal method:

Result of multiplication of all of them will be divisible by each of them

Sounds big number? Let us try to find smallest number.

If we consider 9, a multiple of 9 becomes multiple of 3 as well. So, 3 can be dropped. (So far, we have considered only 9).

If we take 8, multiple of 8 is multiple of 2 and 4 as well.

So, we take 8 and drop 2 and 4. (So, far we have taken 8 and 9, result 8×9=72).

Pending are 5, 6, 7 and 10. Result so far is 8×9, which happens to be multiplie of 6. So, 6 can be dropped.

Result is not multiple of prime number 5. Hence, 5 should be considered. Result so far is 5 × 8 × 9. By the same argument, 7 should be considered. Result so far 5 × 7 × 8 × 9.

Only number left is 10. The number is multiplie of 10 (as it is multiplie of 5 × 8 = 10 × 4; so multiple of 10).

Hence, 10 can be dropped.

The number is 5 × 7 × 8 × 9 = 40 × 63 = 2520.

➺Formal method:

Prime factor of all the numbers are 2, 3, 5 and 7.

The highest power of 2 is 3, of 3 is 2 and 1 each of 5 and 7.

So, common multiple is

23325171

=8×9×5×7

=2520

Ans.: 2520