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  • The least number that is divisible by all the numbers from 1 to 10 is(A) 10 (B) 504(C) 100 (D) 2520

The least number that is divisible by all the numbers from 1 to 10 is:
  (A) 10              (B) 504            (C) 100                        (D) 2520

Answers (1)

Option A is not the answer of the question, because 10 is not divisible by 3, 4, 6, 7, 8, 9
Option B is also not the answer of the question, because 504 is not divisible by 5 and 10
Option (C) is also not the answer of the question because 100 is not divisible by 3, 6, 7, 8 and 9
Option (D) is the answer of the question because 2520 is divisible by all the numbers from 1 to 10.
Calculation:
Prime factorization of all the numbers:
1 = 1
2 = 2
3 =3
4 =2\times2
5 =5
6 = 3\times2
7 = 7
8 = 2\times2\times2
+9 = 3\times3
10 = 2\times5
For LCM, we have to take all the primes from prime factorization of two number.
The common prime in both numbers has to be taken only once.
Therefore,
LCM = 2\times2\times2\times3\times3\times3\times5\times7 =2520
Therefore, option (D) is correct.

Posted by

infoexpert27

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