Solving Ratio and LCM Problems
Let the two numbers be represented based on their given ratio. Since the ratio is 3 : 4, we can denote the numbers as $3x$ and $4x$, where $x$ is a common multiplier.
Calculating the LCM
The Least Common Multiple (L.C.M.) of the two numbers, $3x$ and $4x$, can be calculated. Since 3 and 4 have no common factors other than 1 (they are coprime), their L.C.M. is:
L.C.M.($3x$, $4x$) = L.C.M.(3, 4) $\times$ $x$ = $12x$
Finding the Multiplier 'x'
We are given that the L.C.M. of the two numbers is 180. Therefore, we can set up the equation:
$12x = 180$
To find the value of $x$, divide 180 by 12:
$x = \frac{180}{12}$
$x = 15$
Determining the Numbers
Now, substitute the value of $x$ back into the expressions for the two numbers:
- First number = $3x = 3 \times 15 = 45$
- Second number = $4x = 4 \times 15 = 60$
Identifying the Larger Number
Compare the two numbers calculated:
- The numbers are 45 and 60.
- The larger of the two numbers is 60.
Similar Questions
- If A : B = 3 : 5 and B : C = 4 : 7, then the value of A : B : C is:
- If $a : b :: 3 : 4$ then the value of the expression $\frac{5a - 3b}{7a + 2b}$ is:
- If the third proportional of 8 and 20 be x, then what is the value of x?
- If $0.75 : x :: 25 : 8$, then what is the value of $x$?
- If $a : b = 7 : 9$ and $b : c = 1 : 12$, then $a : b : c$ is:
- If $\frac{A}{4} = \frac{B}{5} = \frac{C}{6}$, then $A : B : C$ is:
- If a map of a city was drawn on a scale of 0.05 centimetre to kilometre, what area would represent a country if it has an area of 8000 square kilometres?
- If A : B = 1 : 3, B : C = 5 : 4 and C : D = 2 : 3, then the value of A : B : C : D will be:
- An amount of money is to be divided between A, B and C in the ratio of 5 : 2 : 8. If the difference between the shares of A and C is ₹7,740, then what will be the total amount?
- If a vessel gets filled by 15 glasses of milk where capacity of each glass is 1.5 L, how many glasses are required to fill the same vessel if the capacity of each glass is 0.5 L?
Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
