Question

what is the least number which is divisible by all the numbers between 1 to 7

Answer 1

Answer:

420

Step-by-step explanation:

We can ignore 1, since any counting number is divisible by 1.

We prime factor each of the counting numbers from 2 to 7

2 = 2

3 = 3

4 = 2*2

5 = 5

6 = 2*3

7 = 7

The LCM of all those must have as many factors of

each prime that appears in any factorization

2 appears at most 2 times as a factor of 4

3 appears at most 1 times as a factor of 3 and 6

5 appears at most 1 time as a factor if 5

7 appears at most 1 time as a factor of 7

So the LCM has

2 factors of 2, 1 factors of 3, and 1 facor each of 5 and 7

LCM = 2*2*3*5*7 = 420