If two numbers are in the ratio 2:3 and their LCM is 60, what is the sum of the

₹0.0

Question: If two numbers are in the ratio 2:3 and their LCM is 60, what is the sum of the two numbers?

Options:

Correct Answer: 40

Solution:

Let the numbers be 2x and 3x. Then, LCM(2x, 3x) = 6x = 60, which gives x = 10. The numbers are 20 and 30, and their sum is 50.

If two numbers are in the ratio 2:3 and their LCM is 60, what is the sum of the two numbers?

If two numbers are in the ratio 2:3 and their LCM is 60, what is the sum of the two numbers?

Step 1: Understand that the two numbers are in the ratio 2:3. This means if we let the first number be 2x, the second number will be 3x.
Step 2: Write down the two numbers: 2x and 3x.
Step 3: Recall that the LCM (Least Common Multiple) of two numbers is given as 60.
Step 4: Calculate the LCM of 2x and 3x. The LCM of 2x and 3x is 6x.
Step 5: Set up the equation: 6x = 60.
Step 6: Solve for x by dividing both sides of the equation by 6: x = 60 / 6 = 10.
Step 7: Substitute x back into the expressions for the numbers: First number = 2x = 2 * 10 = 20, Second number = 3x = 3 * 10 = 30.
Step 8: Find the sum of the two numbers: 20 + 30 = 50.

Ratios – Understanding how to express two quantities in a proportional relationship.
Least Common Multiple (LCM) – Calculating the smallest multiple that is exactly divisible by two or more numbers.
Algebraic Manipulation – Using variables to represent unknown quantities and solving equations.