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