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.
99
Given the ratio of three numbers is 5:7:9 and their LCM is 2835. We need to find the sum of the greatest number and the difference between the first two numbers.
- Let the numbers be 5x, 7x, and 9x.
- The LCM of these numbers is:
LCM = LCM(5x, 7x, 9x) = 315x - Set 315x equal to the given LCM:
315x = 2835
x = 2835 / 315
x = 9 - Thus, the numbers are:
5x = 5(9) = 45
7x = 7(9) = 63
9x = 9(9) = 81 - The greatest number is 81 and the difference between the first two numbers is:
63 - 45 = 18 - The sum of the greatest number and the difference is:
81 + 18 = 99
The required sum is 99, which matches the given correct answer.
Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
