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Q.

The LCM of 54, 90, and a third number is 1890 and their HCF is 18. The third number is


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a

36

b

180

c

126

d

108 

answer is C.

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Detailed Solution

Given numbers are 54, 90, and 1890 and their HCF is 18.
Considering the LCM, three values are 54, 90, and 1890, and the HCF is 18.
Let one of the factor of the third number be x.
Since, 18 is the HCF of all the three numbers,
The factors of 54 and 90 are,
54 = 18×3
90=18Question Image5
So, the LCM of the third number is,
⇒18×3×5×x=1890
⇒270x=1890
⇒x=7
Since, the HCF of the three numbers is 18, so, the third number is 18×7=126.
Therefore, the third number is 126.
Hence, option 3 is correct.
 
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The LCM of 54, 90, and a third number is 1890 and their HCF is 18. The third number is