Question

Which two consecutive even numbers have an LCM of 90?

Answer 1

LCM of two numbers is 90. For LCM question problems, you have to think of two numbers, such that the smallest number that they can both equally divide into is the same. Therefore, two numbers, such that the LCM is 90, would be 5 and 18, or 9 and 10.

Answer 2

The two consecutive even numbers are 10, 12, 18 and 20.

Explanation:

• Consider the two consecutive number be $2x$ and $2x+2$.
• The product of two numbers = HCF × LCM. The HCF of two even number is 2.
• According to the formula we get $2x(2x+2)=2*90$.
• By canceling the 2 and multiplying the $x$ we have $2x^{2} +2x=90$.
• Factorizing the given equation we get $(x+5) (x-9)=0$.
• $x=-5$, $x=9$, $x=-9$ and $x=9$ by neglecting the negative value.
• By substituting the x value in $2x$ and $2x+2$ we have 10, 12, 18 and 20.
• Hence the two consecutive even numbers are 10, 12, 18 and 20.