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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.
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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.
What is the LCM of two numbers that have no common factors than 1 give an example?
The LCM is their product. The LCM of 27 and 35 is 945.
What are 2 numbers that have the LCM of no common factors that are greater than one?
Two numbers that have no common factors greater than one are considered co-prime or relatively prime. Their LCM is their product.
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 are lcm and gcf alike?
The greatest common factor, or GCF, is the largest positive integer that will divide evenly with no remainder into all the members of a given set of numbers. The least common multiple, or LCM, is the smallest positive integer that all the members of a given set of numbers will divide into evenly with no remainder. Factors go into numbers, numbers go into multiples.
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.
How can you determine whether the LCM of two numbers is the product of the numbers or is less than the product if the numbers?
By finding out whether they have any factors in common. If the only factor they have in common is 1, the LCM will be their product. If they have more factors in common, their LCM will be less than their product.
How can you determine whether the LCM of two numbers is the product of the numbers or is less than the product of the numbers explain?
If the two numbers have no common factors other than 1, the LCM will be their product. If there are other common factors, the LCM will be less.
What is the LCM of two numbers that have no common factors?
Their product.
How can you determine from the prime factorization whether the least common multiple of two numbers is the product of the number?
If the two numbers have no common prime factors, the LCM will be the product of the numbers.
Is The LCM of two numbers that have no common factors is their product?
Yes, this is true
What is the LCM of two numbers that have no common factors greater that 1?
Their product.
What is the LCM of two numbers that have no common factors than 1 give an example?
The LCM is their product. The LCM of 27 and 35 is 945.
What is the LCM of the numbers 3 and 8?
These numbers do not share any common factors hence the least common multiple is the product-24.
What is the LCM of 2 numbers that have no common factors greater than 1?
Their product.
Why do some numbers have their LCM and their product the same?
If the two numbers do not have any factors in common (other than 1), then the LCM is the same as the product of the two numbers. Example: LCM of 5 & 6 is 30, which is the same as the product.
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.
