Find Two Numbers by Ratio and LCM Calculator

Welcome to the free online calculator to find two numbers by given ratio and LCM. For example, the ratio of two numbers is 3:4 and their LCM is 120. What are the numbers?

LCM stands for least common multiple, which refers to the smallest positive integer that is divisible by 2 numbers. It is called by many names – Lowest Common Multiple (LCM), Smallest Common Divisor (SCD), Lowest Common Denominator (LCD) and Least Common Factor (LCF).

Now, how to solve the problem mentioned above?

There are two methods, one is the assumption method and the other is the factor method. In the following, a detailed description will be given in conjunction with the above example.

Method 1: Assumption method

The ratio of these two numbers is 3:4. Therefore, we can assume that the two numbers are 3x and 4x. Obviously, x is their HCF.

According to the formula, the product of two numbers is equal to the product of their LCM and HCF.

Products of the two numbers = LCM * HCF

Substitute the assumed numbers into the formula.

Products of the two numbers = LCM * HCF

3x * 4x = LCM(3x, 4x) * x

According to the question, the LCM is 120, put it into the equation and solve.

3x * 4x = 120 * x

12x = 120

x = 10

So, the two numbers are 3x = 30 and 4x = 40.

Let’s verify.

30:40 = 3:4

LCM(30, 40) = 120

Correct.

Method 2: Factor method

Since the LCM of two numbers is 120, the two numbers must be factors of 120. So, we can calculate the factors of 120 first. Then, find the two numbers in the factors whose ratio is 3:4.

With the find all factors calculator, we can easily get the factors of 120 are

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

Among them, there are 4 pairs of two numbers whose ratio is 3:4.

(3, 4), (6, 8), (15, 20), (30, 40)

The LCM of 3 and 4 is 12. Ineligible.

The LCM of 6 and 8 is 24. Ineligible.

The LCM of 15 and 20 is 60. Ineligible.

The LCM of 30 and 40 is 120. Correct.

So, the two numbers are 30 and 40.

Obviously, the first method is better than the second method. However, the steps are a little boring. So, we developed this free calculator to find two numbers by given ratio and LCM. No calculations required and displays the answer in milliseconds.

Next, we will introduce how to use the calculator.

Using the calculator is simple, follow these 3 steps:

Next, let’s look at some examples.