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
Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
A and B are two prime numbers such that A > B and their LCM is 209. The value of A 2 - B is:
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
