Question

Which two
consecutive even numbers have an LCM of 180
​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

✪ANSWER✪

• The two consecutive even numbers are 18 and 20.

★EXPLAINATION★

᯽CONCEPT᯽

For any integer a, b

HCF(a, b) = HCF(a, a-b)

✫CALCULATION✫

Let x and x+2 be the two consecutive even numbers, then

$\to LCM\:of\:x, (x+2) = 180$

$\to HCF\:of\:(x, (x+2))$

$= HCF\:of\:(x, (x+2)-x)$

$= HCF\:of\:(x, 2)$

$= 2$(Since x is even)

Also,

$\to x(x+2) = HCF\times LCM$

$\to x(x+2) = 2\times 180$

$\to x^2 +20x - 18x - 360 = 0$

$\to x(x +20) - 18(x +20) = 0$

$\to (x +20)(x - 18) = 0$

$\to x = 18$

Thus, the two conswcutive numbers are 18, 20.