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
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 ?
A bag contains Rs. 420 in the form of 5 rupee, 2 rupee, and 1 rupee coins. The number of coins of 5 rupee, 2 rupee, and 1 rupee is in the ratio of 2 : 3 : 5. What is the total number of coins in the bag?
If P/Q = 8/9 and Q - P = 12, then what is the value of P?
A child gets 1 random coin out of Re 1, Rs 2, and Rs 5 coins daily. He starts on 1st April and at the end of the month, he has coins in the ratio 5 ∶ 4 ∶ 6. Find the value of the coins with him
Find the proportion equivalent to M : N : O : P if M : N = 8 : 15, N : O = 5 : 9 and O : P = 18 : 19 ?
