Question

Find the least number that is divisible by all the number from 1 to 10 [ both inclusive].
PLEASE SOLVE THIS QUESTION WITH STEP BY STEP...​

Answer 1

Answer:

2520

least number divisible by all numbers from 1 to 10 = LCM of 1,2,3,4,5,6,7,8,9,10

1 = 1

2 = 2

3 = 3

4 = 2*2

5 = 5

6 = 2*3

7 = 7

8 = 2*2*2

9 = 3*3

10 = 2*5

LCM = 2*2*2*3*3*5*7.

= 2520

Answer 2

⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

2520

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

• The least number divisible by all the numbers from 1 to 10.

${\rm{\purple{\underline{\underline{Concept \: Used: }}}}}$

• To find out the least number divisible by all the numbers from 1 to 10 we have to find out the least common multiple (LCM) of number from 1 to 10.

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

Now, let's prime factorise numbers from 1 to 10 as we need to find their least common multiple.

1 = 1 × 1

2 = 2 × 1

3 = 3 × 1

4 = 2 × 2 = 2²

5 = 5 × 1

6 = 2 × 3

7 = 7 × 1

8 = 2 × 2 × 2 = 2³

9 = 3 × 3 = 3²

10 = 2 × 5

Now, the least common multiple of the number from 1 to 10 = product of each factor by the maximum number of time it appears in the prime factorization.

= 1 × 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7

= 1² × 2³ × 3² × 5 × 7

= 1 × 8 × 9 × 5 × 7

= 2520

Hence, the least number that is divisible by all the numbers from 1 to 10 is 2520.