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Why does the product of 2 numbers equal the product of its LCM and GCF?
Wiki User
∙ 10y ago
It's easier to see with prime factorizations. Consider 30 and 42.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Their product is (2 x 3 x 5)(2 x 3 x 7) = 1260
Their GCF is 2 x 3
Their LCM is 2 x 3 x 5 x 7
That product is (2 x 3)(2 x 3 x 5 x 7) = 1260
Consider two prime numbers, 5 and 7.
Their product is 35.
Their GCF is 1.
Their LCM is 35.
That product is also 35.
Wiki User
∙ 10y ago
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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.
How will I find a number when the LCM is 252 and HCF is 14 and the first number is 28?
The product of the GCF and LCM of two numbers is equal to the product of the two numbers. The other number is 126.
Hcf of two numbers is 87 and their LCM is 24960 if one of two numbers is 348 find the other number?
As a general rule, the product of the GCF and the LCM is equal to the product of the original numbers. That would make the answer to this problem 6240. Unfortunately, the GCF of 348 and 6240 isn't 87 and their LCM isn't 24960. Someone notated this problem incorrectly.
What is the product of two numbers is 2700 their GCF is 15 what is the LCM?
Their LCM is 2700/(15^2) = 180.
Why is the product of the LCM and HCF the same as the product of the original pair of numbers?
It's the way numbers work. Consider 32 and 33. Consecutive integers are relatively prime, that is, their GCF is 1. If two numbers have a GCF of 1, the LCM will be their product. 32 x 33 = 1056 1 (GCF) x 1056 (LCM) = 1056 2 x 528 = 1056 3 x 352 = 1056 4 x 264 = 1056 Notice the pattern. As the GCF increases, the LCM decreases. Consider 32 and 34. Consecutive even numbers have a GCF of 2. The LCM of 32 and 34 is 544. 32 x 34 = 1088 2 (GCF) x 544 (LCM) = 1088 If you know either the GCF or the LCM of two numbers, you can find the other one without factoring again. The GCF of 28 and 36 is 4. Their product is 1008. Their LCM is 1008 divided by 4, or 252.
What is the product of the GCF and LCM of two numbers?
The product of the GCF and LCM of a pair of numbers is equal to the product of the 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.
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.
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 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.
What relationship does the GCF have with LCM?
It's kind of inverse. The product of the GCF and LCM of a pair of numbers will equal the product of the original numbers.
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.
What is the Multiplication of HCF and LCM of two number?
The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers.
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.
How do you find the other number when the one number is given with the LCM and the GCF?
The product of the original numbers is equal to the product of the GCF and LCM. Divide the product of the LCM and GCF by the one number. The answer will be the other.
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.
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.
