Question

what is the least number that is divisible by all numbers between 1 and 10(both inclusive)

Answer 1

Hey there !

Solution:

To find the least number divisible by numbers from 1 to 10, we need to know their LCM.

To find LCM let us write the prime factorisation for all the numbers.

=> 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 = Product of all numbers with their highest powers.

Numbers are: 2, 3, 5 and 7

LCM = 2³ × 3² × 5 × 7

=> LCM = 8 × 9 × 35

=> LCM = 72 × 35

=> LCM = 2520

Hence the answer is 2520.

Option ( a ) is the right answer.

Hope my answer helped !