Question
The HCF of two numbers is 18 and their LCM is 540. If
one of the numbers is 90, find the other number.Solution
For two numbers a and b: a × b = HCF × LCM Let the other number be x. 90 × x = 18 × 540 Compute RHS: 18 × 540 = 18 × (54 × 10) = (18 × 54) × 10 18 × 54 = (20 − 2) × 54 = 1,080 − 108 = 972 So 972 × 10 = 9,720 So 90x = 9,720 x = 9,720 / 90 = 108 Answer: The other number = 108.
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