find the smallest number who is multiple of all natural numbers from 2 to 10
Answers
20×19×18×17×16×15×14×13×12×11=required number
2520 is the smallest number who is multiple of all natural numbers from 2 to 10
Solution:
Given that,
We have to find the smallest number who is multiple of all natural numbers from 2 to 10
Which means, we have to take least common multiple of numbers from 2 to 10
That will be the smallest number who is multiple of all natural numbers from 2 to 10
FIND LCM OF NUMBERS FROM 2 TO 10
List all prime factors for each number.
Prime Factorization of 2 shows: 2 is prime
Prime Factorization of 3 shows: 3 is prime
Prime Factorization of 4 is: 2 x 2
Prime Factorization of 5 shows: 5 is prime
Prime Factorization of 6 is: 2 x 3
Prime Factorization of 7 shows: 7 is prime
Prime Factorization of 8 is: 2 x 2 x 2
Prime Factorization of 9 is: 3 x 3
Prime Factorization of 10 is: 2 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
2, 2, 2, 3, 3, 5, 7
Multiply these factors together to find the LCM
LCM = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520
Thus 2520 is the smallest number who is multiple of all natural numbers from 2 to 10
Learn more:
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