Three numbers are in the ratio of 2 : 5 : 7, and their least common multiple (LCM) is 1050. Determine their greatest common divisor (GCD).
15
The numbers are in the ratio 2 : 5 : 7. Their LCM is 1050. We can express these numbers as 2x, 5x, and 7x. The LCM of 2x, 5x, and 7x is the LCM of 2, 5, and 7, multiplied by x. We know that the LCM of 2, 5, and 7 is 70, so 70x = 1050. Thus, x = 15. The three numbers are 30, 75, and 105. The GCD of 30, 75, and 105 is 15.
Important Questions from Simple Ratios
The ratio of two numbers is 9 : 5. If 8 is added to the larger number and 4 is subtracted from the smaller number, the greater number becomes twice the smaller number. The larger number is:
Divide 500 into two parts such that the ratio of one to the other are in 5 : 3?
The ratio of the number of men and women in a company is 5 : 4. If the number of men and women increase by 16% and 15%, respectively, then what will be the new ratio of men and women ?
The monthly salaries of an officer and a clerk are in the ratio 11 : 4. If the monthly salary of the officer increases by ₹7,000 and that of the clerk by ₹3,000, then the ratio becomes 19 : 7. What was the initial salary (in ₹) of the officer?
If X : Y = 7 : 5 and Y : Z = 7 : 11, then what is the ratio of X : Y : Z?
