Question
Download Solution PDFThe least common multiple of two numbers is 138. But their GCD is 23. The numbers are in the ratio 1 : 6. Which is the largest number among the two?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation -
Let's denote the two numbers as x and 6x because they are in the ratio of 1:6.
We're given that the least common multiple (LCM) of x and 6x is 138 and their greatest common divisor (GCD) is 23.
We know that the product of two numbers equals the product of their GCD and LCM:
Product of two number = GCD X LCM
x x 6x = 23 x 138
6x2 = 3174
x2 = 3174/6 = 529
x = 23
So, the smaller number x is 23, and the larger number 6x is 6 x 23 = 138.
Therefore, the larger number among the two is 138.
Last updated on Jan 29, 2025
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