Answer:
Two consecutive even terms and LCM = 180
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∗b=HCF∗LCM - (i)
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 of ‘2x’ and ‘2x + 2’ is ‘2’ - (ii)
Therefore,
from (i) and (ii),
2x∗(2x+2)= HCF * LCM
2x∗(2x+2)=2∗180
x∗(2x+2)=180
2x2+2x−180=0
Solving the quadratic equation we get,
x=9,−10 (we discard -10 since it is negative)
Therefore, the numbers are
2∗9=18 (1st no.)
2∗9+2=18+2=20 (2nd no.)
Answer : 18,20
Explanation: