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
If the value of \(\frac{{p - q}}{q} = \frac{4}{3}\) .find p : q
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
The two numbers are in the ratio of 9 ∶ 7 and the difference between of these two number is 6000. What is the sum of the two numbers?
A certain number is added to each of a pair of numbers which are in the ratio 4 ∶ 5. The sum of the resulting numbers is 39 and their ratio (taken in the same order as mentioned above) is 6 ∶ 7. What is the number added?
If (p + q) ∶ (q + r) ∶ (r + p) = 5 ∶ 6 ∶ 7 and p + q + r = 18, find the value of p ∶ q ∶ r
