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 A and B is 5 : 8. If 5 is added to each of A and B, then the ratio of A and B becomes 2 : 3. The sum of A and B is:
The ratio of two numbers A and B is 5: 8. If 5 is added to each of A and B, then the ratio becomes 2 : 3. The difference between A and B is:
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The ratio of monthly incomes of A and B is 4 ∶ 5 and that of their monthly expenditures is 3 ∶ 8. If the income of A is equal to the expenditure of B, then what is the ratio of savings of A and B?
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