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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.
When is the product of three integers larger than either of them?
"Either" is used for two. I'll assume that you mean "larger than ANY of them". The following applies to ANY real numbers.For TWO numbers, the product is larger than either of them if both numbers are greater than one. For THREE numbers, the product is larger than any of them if the two numbers OTHER than the largest number have a product greater than one. For example: 0.5, 3, 5 The largest number here is 5; the product of the OTHER two is 0.5 x 3 = 1.5. Or here is an example with integers: -5, -3, 10 The product of the "other two" numbers is 15, which is larger than one - so the product of all three is larger than the largest number (and therefore, larger than ANY of them). Another example: -5, 1, 10 The product of the two numbers OTHER than the largest is -5 x 1 = -5; since this is NOT greater than 1, the product of all three is NOT greater than any of the numbers. This reasoning can be extended to four or more numbers. For 4 numbers: If the product of all three numbers OTHER than the largest one is GREATER than one, then the product of ALL FOUR numbers is greater than ANY of them.
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 it possible for the product of two prime numbers to be odd?
More than possible. Unless one of your prime numbers is 2, the product of any other two will be odd.
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.
The product of two numbers that are less than zero is also less than zero.?
No. The product of two negative numbers is positive.
Is the product of two positive mixed numbers less than one?
No, the product of two positive mixed numbers can never be less than one.
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 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.
Product of 2 prime numbers is equal to product of 2 other prime numbers?
No, the product of two prime numbers is unique.
What is true about the product of two even numbers?
The product of two even numbers is even. The product of two even numbers will be even. If they are both positive numbers, it will be greater than both of them. If one of them ends in 0, the product will end in 0.
When is the product of two nonzero integers less than or equal of the two factors?
When one of the numbers is positive and the other is negative.
