Foundation
Mathematics Foundation
Inequalities
HCF and LCM
Properties of Real Number
Question
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is
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Solution
Given the LCM two numbers 54, 90 and third number is 1890 and HCF is 18
Let the number is 18x because one factor is also 18 the common factor HCF
Then factor 54,90 ,18 = 18 × 3,18 × 5,18 × 18 × x
∴ 18 × 3 × 5 × x = 1890 ⇒ 270 x = 1890 ⇒ x = 7
Then third number is 18 × 7 = 126