Find Two Numbers by Product and LCM Calculator

Welcome to the free online calculator to find two numbers by given product and LCM. For example, the product of two numbers is 320 and their LCM is 80. What are the numbers?

Find Two Numbers by Product and LCM Calculator

x * y = a

LCM(x, y) = b

Eg, The product of two numbers is 320 and their LCM is 80. What are the numbers? Enter 320 in the first input box and enter 80 in the second input box. Then click Calculate button.

Calculate Reset

How to find two numbers based on the given product and LCM

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 factor method and the other is the factor pair method.

Method 1: Factor method

Since the LCM of two numbers is 80, the two numbers must be factors of 80. So, we can calculate the factors of 80 first. Then, find the two numbers in the factors whose product is 320.

With the find all factors calculator, we can easily get the factors of 80 are

1, 2, 4, 5, 8, 10, 16, 20, 40, 80

Among them, there are 3 pairs of two numbers whose product is 320.

4 * 80 = 320

8 * 40 = 320

16 * 20 = 320

The LCM of 4 and 80 is 80. Correct.

The LCM of 8 and 40 is 40. Ineligible.

The LCM of 16 and 20 is 80. Correct.

So, the two numbers are (4, 80) or (16, 20).

Method 2: Factor pair method

Because the product of two numbers is 320. So, these two numbers must be factors of 320, a pair of factors.

Therefore, we can calculate the pair factors of 320 first. Then, find the pair of factors whose LCM is 80.

With the find all factors calculator, we can easily get the pair factors of 320 are

(1, 320), (2, 160), (4, 80), (5, 64), (8, 40), (10, 32) and (16, 20)

The next problem is simple, just find out that the LCM of the pairing factors is 80.

Obviously, we can also get the answer to be (4, 80) or (16, 20).

Well, these are two common solutions that, each method needs to calculate the factors, and then judge. So, we developed this free calculator to find two numbers by given product and LCM. No calculations required and displays the answer in milliseconds.

Next, we will introduce how to use the calculator.

How to use the calculator to find two numbers by product and LCM

Using the calculator is simple, follow these 3 steps:

1Enter the product in the first input box.
2Enter the LCM in the second input box.
3Click Calculate button to get the answer, or click Reset button to start a new calculation.

Next, let’s look at some examples.

Solved examples using the calculator to find two numbers by product and LCM

Example 1: The product of two numbers is 2208 and their LCM is 552. What are the numbers?

Enter 2208 in the first input box.

Enter 552 in the second input box.

Then click Calculate button, as shown in the figure, the two numbers are (4, 552) or (8, 276) or (12, 184) or (24, 92).

4 * 552 = 2208

LCM(4, 552) = 552

Or

8 * 276 = 2208

LCM(8, 276) = 552

Or

12 * 184= 2208

LCM(12, 184) = 552

Or

24 * 92 = 2208

LCM(24, 92) = 552

The product of two numbers is 2208 and their LCM is 552. What are the numbers?

Example 2: The product of two numbers is 2560 and their LCM is 320. What are the numbers?

Enter 2560 in the first input box.

Enter 320 in the second input box.

Then click Calculate button, as shown in the figure, the two numbers are (8, 320) or (40, 64).

8 * 320 = 2560

LCM(8, 320) = 320

Or

40 * 64 = 2560

LCM(40, 64) = 320

The product of two numbers is 2560 and their LCM is 320. What are the numbers?

Find Two Numbers by Product and LCM Calculator