(ii) What message does the White Chief send to the native people?
Answers
18,20 are two consecutive even numbers.
Step-by-step explanation:
Given: Two consecutive even terms and LCM = 180
To find : Consecutive numbers
Let’s assume the two terms:
1st term : 2x
2nd term : 2x + 2
There is a rule which states that :
→ If ‘a’ and ‘b’ are two numbers, then their product is equal to the product of their LCM and HCF.
i.e, a\times b=\text{HCF} \times \text{LCM}a×b=HCF×LCM .......[1]
We can logically say that the HCF of any two consecutive even numbers is always equal to ‘2’ provided that the smallest no. is at least ‘2’.
i.e, HCF= 2 ..........[2]
From [1] and [2],
2x\times(2x+2) =\text{HCF} \times \text{LCM}2x×(2x+2)=HCF×LCM
4x^2+4x=2 \times 1804x
2
+4x=2×180
x^2+x=90x
2
+x=90
x^2+x-90=0x
2
+x−90=0
Solving the quadratic equation by middle term split we get,
x^2+10x-9x-90=0x
2
+10x−9x−90=0
x(x+10)-9(x+10)=0x(x+10)−9(x+10)=0
(x+10)(x-9)=0(x+10)(x−9)=0
x=9,−10(we discard -10 since it is negative)
Therefore, the numbers
1st term : 2x =2×9=18
2nd term : 2x + 2 =2×9+2=18+2=20
Therefore, 18,20 are two consecutive even numbers.