Question

find the least number that is divisible by all numbers between 1 and 10​

Answer 1

Step-by-step explanation:

The least number which is divisible by all numbers between 1 to 10 is

2,520

2520 is the least number which is divisible by all numbers between 1 to 10 .

Proof :-

Prime factors of all numbers from 1 to 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

In the prime factors no.of times the digits appeared

'2' appeared 3 times as in factor 8

'3' appeared 2 times as in factor 9

'5' appeared 1 time as in factor 5 & 10

'7' appeared 1 time as in factor 7

LCM = 3 factors of 2 × 2 factors of 3 × 1 factor each of 5 & 7

LCM = 2 × 2 × 2 × 3 × 3 × 5 × 7

LCM = 2³ × 3² × 5¹ × 7¹

LCM = [ ( 8 × 9 ) × ( 5 × 7 ) ]

LCM = 72 × 35

❤️LCM = 2,520