## which two consecutive even numbers have an LCM of 180​

Question

which two consecutive even numbers have an LCM of 180​

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9 months 2021-08-12T08:12:54+00:00 2 Answers 0 views 0

Which two consecutive even numbers have an LCM of 180?

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Given: 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

2×2+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.)