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the sum of 5 concecutive numbers is 35. what is the lcm of these 5 numbers.

Sagot :

Five  consecutive numbers:

Let first number: x
      second number: x + 1
      third number:  x + 2
      fourth number: x + 3
      fifth number: x + 4

The sum of the numbers is 35.

(x) + (x+1) + (x+2) + (x + 3) + (x+4) = 35
5x + 10 = 35
5x = 35 - 10
5x = 25
 5      5
x = 5  

First Number: x = 5
Second number: x + 1 
                              5 + 1 = 6
Third number: x + 2 
                          5 + 2 = 7
Fourth number:  x + 3
                             5 + 3 = 8
Fifth number:  x + 4
                         5 + 4 = 9

The five numbers are: 5, 6, 7 ,8, 9

Their LCM, prime factorization:
5 = 5 × 1
6 = 2×3
7 = 7×1
8 = 2×2×2
9 = 3 × 3
 
Cancel the factors that appeared in other number, that it, the factors of second number 6 have appeared in factors of numbers 8 and 9

LCM : 5 × 7 × 2³ × 3² = 2,520.

LCM = 2,520