Question

Find the least number which is divisible by all number from 1 to 10 ( both inclusive)
$\frac{yx)06.22626616 \div - { { \times \times {2232222222 \frac{2...... \times \times \times \times }{?} }^{2} }^{2} }^{2} }{?} hhikk log_{ log_{ \sec( \sin( \tan( \sec( \sec( \binom{ \binom{ \binom{ \binom{ \binom{ \binom{ \binom{ \binom{\% \infty }{?} }{?} }{?} }{?} }{?} }{?} }{?} }{?} ) ) ) ) ) }(?) }(?) \times \frac{?}{?} u$

Answer 1

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The least no. which is divisible by all the numbers between 1 to 10 is the LCM of all these no.s
We want LCM (1 2 3 4 5 6 7 8 9 10)
We can ignore 1 as any counting no. is divisible by 1
Prime factor of each of the following no.s from 2 to 10
2=2
3=3
4=2×2
5=5
6=2×3
7=7
8=2×2×2
9=3×3
10=2×5
The LCM of all those must have as many factors of each prime tht appears in any factorization
2.....(3 times).....(factor of 8)
3.....(2 times).....(factor of 9)
5.....(1 time) .......(factor of 5 and 10)
7.......(1 time) .......(factor of 7)
So, LCM has
2 factors of 3, 3 factors of 2, and 1 factor each of 5 and 7
LCM = 2×2×2×3×3×5×7
= 2520....
Therefore, the least no. which is divisible by all the numbers between 1 to 10 is 2520

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