The LCM of two numbers is sometimes the product of the two numbers.
Not always. The product of two numbers will always be a common multiple, but it will not always be least. The product of 4 and 9 is 36. The LCM of 4 and 9 is 36. The product of 4 and 8 is 32. The LCM of 4 and 8 is 16.
Sometimes true.
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.
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.
The prime factorization of the LCM will contain all the prime factors of the two original numbers. When the original numbers don't have any prime factors in common, (the GCF is 1) the LCM will be their product. When the two original numbers have prime factors in common (the GCF is 2 or more) the duplicates will be discarded and the LCM will be less than their product.
Not always. The product of two numbers will always be a common multiple, but it will not always be least. The product of 4 and 9 is 36. The LCM of 4 and 9 is 36. The product of 4 and 8 is 32. The LCM of 4 and 8 is 16.
Sometimes, not always.
Yes.
Numbers that are relatively prime have their LCM as their product.
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.
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.
The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers.
The LCM of two consecutive numbers is always the product: 32 times 33=1056 1056=LCM
Sometimes true.
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.
Sometimes.
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.