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Why are the multiples of any number other than one not prime numbers?
The multiples of any number cannot be prime numbers because such numbers are the product of at least two numbers. Prime numbers, but definition, cannot be cannot be the product of any numbers except itself and one.
Why do you think the least common multiple is not always the product of the two numbers?
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.
Is even number times even number always even?
Yes, it is. Any whole number times an even number will be even. This is because whole numbers can be represented as the product of their prime factors. Every even number contains 2 as a prime factor (thereby excluding all even numbers above 2 from being prime.) Additionally, the product of any two numbers is equal to the product of their prime factors. This means that the result of multiplying an even number by a whole number will always have a prime factor of 2, making it an even number.
Can a prime number be multiple of any other number except itself explain why or why not?
A prime number can be multiplied by any other numbers because all whole numbers are the product of prime numbers.
Can you find the LCM of a prime number?
No. You can only find the LCM of at least two numbers, prime or otherwise. The LCM of any two prime numbers is their product.
