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The sum of three consecutive even numbers is 24. What is the least common multiple of these three numbers?
24÷3=8
8＋2=10
8-2=6
These three numbers are 6, 8 and 10
The least common multiple is 80
The sum of three consecutive even numbers is 24, and the least common multiple of these three numbers is______ ．
24 △ 3 = 8, then the other two even numbers are 8-2 = 6, 8 + 2 = 10, then the three even numbers are 6, 8 and 10, 8 = 2 × 2 × 2, 6 = 2 × 3, 10 = 2 × 5, so the least common multiple of 6, 8 and 10 is 2 × 2 × 2 × 3 × 5 = 120
If the least common multiple of three consecutive even numbers is 1008, then the sum of the three natural numbers is______ ．
1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7; among the three consecutive even numbers, there is and only one is a multiple of 3. First consider 18, then another is a multiple of 7, 14, the other is 16.2 × 7 = 14; 3 × 3 × 2 = 18; then the remaining even number is 16; the three even numbers are 14, 16, 18, and 14 + 16 + 18 = 48; so the answer is: 48
The reciprocal of the sum of six consecutive even numbers is one in forty-two
Let the six even numbers be x, x + 2, x + 4, x + 6, x + 8, x + 10, respectively
1/（x+x+2+x+4+x+6+x+8+x+10）=1/42
1/（6x+30）=1/42
The solution is x = 2
The six even numbers are 2,4,6,8,10,12 respectively
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