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
- ₹28,000 were divided among A, B and C, such that 2 times the share of A = 9 times the share of B = 6 times the share of C. Find the share of A.
- Which of the following ratios is the greatest?
- The ratio of the incomes of Barun and Anil is $12 : 13$ and that of their expenditures is $10 : 13$. Find the income of Barun and Anil, if they save $₹2100$ and $₹1,300$, respectively.
- What is the simplest form of the ratio of $6\text{ h} : 3\text{ days}$?
- Two natural numbers are in the ratio of $6 : 8$ and their product is $768$. The smaller of the numbers is:
- Two numbers are in the ratio 2 : 3; if 20 is added to 20% of the smaller number, it will be equal to 10% of the larger number plus 25. Then, the smaller number is: _______.
- The ratio of income of Aamir to that of Ali is 5 : 3 and they expend in the ratio of 9 : 5 respectively. If Aamir saves ₹2,600 and Ali saves ₹1,800, Then their respective incomes are:
- If A : B = 3 : 5 and B : C = 4 : 7, then the value of A : B : C is:
- If the third proportional of 8 and 20 be x, then what is the value of x?
- If the third proportional of 25 and 35 be x, then what is the value of x?
Important Questions from Ratio and Proportion
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
