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When is the LCM of 2 numbers equal to the product of the 2 numbers?
Wiki User
∙ 11y ago
When the two numbers are relatively prime.
Wiki User
∙ 11y ago
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Is the product of the 2 original numbers equal to the product of the HCF and the LCM?
Yes.
Why is the least common multiple of 2 prime numbers their product?
Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.
Why is the LCM of 12 and 13 the same as there product but the LCM of 12 and 14 is not the same as there product?
The LCM is the product of the two numbers divided by their HCF. With 12 and 13, the HCF is 1. Therefore, the LCM will equal the product. With 12 and 14, the HCF is 2. Therefore, the LCM will be half of the product.
Is it true that the LCM of 2 numbers is the product of the 2 numbers?
Only if the numbers are co-prime.
What are two numbers whose LCM is less than their product?
The LCM of 4 and 6 is 12.
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.
Is the product of the 2 original numbers equal to the product of the HCF and the LCM?
Yes.
What set of 3 numbers whose LCM is the product of the number?
The set of three numbers whose LCM (Least Common Multiple) is equal to the product of the numbers would be {1, 2, 2}. Here's how it works: LCM(1, 2, 2) = 2, which is also the product of the numbers (1 * 2 * 2 = 4).
Why is the least common multiple of 2 prime numbers their product?
Because prime numbers don't have any common prime factors. Their GCF is 1. Since the product of the GCF and LCM of a pair of numbers equals the product of the numbers, the LCM has to be equal to the product.
What is the product of the GCF and LCM of 4 and 6?
2 x 12 = 24, but there's an easier way if you remember that the product of the GCF and LCM of a pair of numbers will always be equal to the product of the two numbers.
How can you determine if the least common multiple of 2 numbers is the product of the 2 numbers or less than the product of the 2 numbers?
If the GCF of a given pair of numbers is 1, the LCM will be equal to their product. If the GCF is greater than 1, the LCM will be less than their product. Or, stated another way, if the two numbers have no common prime factors, their LCM will be their product.
Why is the LCM of 12 and 13 the same as there product but the LCM of 12 and 14 is not the same as there product?
The LCM is the product of the two numbers divided by their HCF. With 12 and 13, the HCF is 1. Therefore, the LCM will equal the product. With 12 and 14, the HCF is 2. Therefore, the LCM will be half of the product.
What is the LCM of 2 consecutive even numbers?
Their GCF will be 2. Their LCM will be half their product.
Is the LCM of 2 numbers the product of the 2 numbers?
Sometimes, not always.
What is the LCM of 2 consecutive numbers?
Their product.
Is it true that the LCM of 2 numbers is the product of the 2 numbers?
Only if the numbers are co-prime.
Is the LCM of two numbers that have no common factors their product?
The LCM of two numbers is one of the numbers when one of the numbers is a multiple of the other. The LCM of two numbers is the product of the numbers when they are relatively prime. In all other cases (like consecutive even numbers that aren't 2 and 4) the LCM is as you describe.
