The ratio of three numbers is 5 : 7 : 9 and their LCM is 2835. Find the sum of the greater number and the difference between the first two numbers.
Given:
Ratio of three numbers = 5 : 7 : 9
Their LCM = 2835
Solution:
If numbers are in ratio a : b : c, then numbers = 5k, 7k, 9k.
LCM = LCM of (5,7,9) × k
Required sum = (greater number) + (difference of first two numbers).
= 5k, 7k, 9k
LCM of (5,7,9) = 315
So,
LCM of actual numbers = 315k
Equating given LCM
315k = 2835
k = = 9
Actual numbers
5k = 45, 7k = 63, 9k = 81
Greater number = 81
Difference between first two numbers = 63 - 45 = 18
Answer = 81 + 18 = 99
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