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# What is the product of the GCF and LCM of two numbers?

Updated: 9/16/2023 Wiki User

8y ago

The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers. Wiki User

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Q: What is the product of the GCF and LCM of two numbers?
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### How do you find the LCM using GCF?

The GCF of two numbers multiplied by their LCM will equal the product of the original numbers. If you know the GCF, divide it into the product of the two. The result will be the LCM. If the GCF of two numbers is 1, the LCM is their product.

### How do you change GCF into a LCM with 3 numbers?

The product of the GCF and the LCM is the same as the product of the original two numbers. Divide the product of the original numbers by the GCF. The result will be the LCM.

### What is the relationship does the greatest common factor and the LCM have?

The product of the GCF and LCM is equal to the product of the original two numbers.

### What is the relation between HCF and LCM?

Since the product of two numbers is equal to the product of their GCF and LCM, the GCF of two numbers is equal to their product divided by their LCM and their LCM is equal to their product divided by their GCF.

### How do you find GCF knowing LCM?

The LCM of two numbers multiplied by their GCF will equal the product of the original numbers. If you know the LCM, divide it into the product. The result will be the GCF.

### How do you find two numbers if HCF and LCM are known?

The product of the GCF and the LCM of two numbers is equal to the product of the original two numbers. Multiply the GCF and the LCM. The original two numbers will be another factor pair of that total. Find the factor pair that has that GCF and LCM.

### Why does dividing the product by the GCF always give you the LCM?

In number theory, the product of two positive integers will equal the product of their GCF and LCM. Dividing that product by one of them will give you the other.

### What is a simalaritie between GCF and LCM?

They have an inverse relationship. Since the product of the LCM and GCF of two numbers equals the product of the original two numbers, as the GCF increases, the LCM decreases and vice versa.

### What do LCM and GCF have in common?

They are both found from the relationships between the members of a given set of numbers. They have kind of an inverse relationship. Since the product of the LCM and GCF of two numbers is equal to the product of the original numbers, when the GCF increases, the LCM decreases and vice versa.

### How can yo determine whether the LCM of two numbers is the product of the numbers or less than the product of the numbers?

If their GCF is 1, their LCM is their product. If their GCF is greater than 1, their LCM is less than their product.

### How do you check lcm answer?

One way to check: The product of the original two numbers is equal to the product of their GCF and LCM. If you divide that product by their GCF, you will get the LCM.

### If the GCF of two numbers is 15 and their product is 300 what is their LCM?

The general rule is that the product of the LCM and the GCF is equal to the product of the original two numbers. That would make the answer 20. Lets overlook the fact that two numbers with a GCF of 15 and an LCM of 20 don't exist.