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 HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
