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# How can you determine from the prime factorizations whether the least common multiple of two numbers is the product of the numbers or is less than the product of the two numbers?

Updated: 8/20/2019

Tgirlrunit

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9y ago

If none of the prime factors are in common, the LCM will be the product of the two.

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9y ago
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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: How can you determine from the prime factorizations whether the least common multiple of two numbers is the product of the numbers or is less than the product of the two numbers?
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### How can you determine from the prime factorization whether the least common multiple of two numbers is the product of the numbers?

If the prime factorizations have no factors in common, the LCM is the product 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 the product of two whole numbers called a multiple?

The result of multiplying two whole numbers is called a product. It is a multiple of each of the whole numbers.

### To determine the product?

Multiply the numbers

### How can you determine from the prime factorizations whether the least common multiple of two numbers?

Example: 30 and 42Factor them.2 x 3 x 5 = 302 x 3 x 7 = 42Combine the factors, eliminating duplicates.2 x 3 x 5 x 7 = 210, the LCMIf there are no common prime factors, the LCM is the product of the original two numbers.

### Is the product of two counting numbers a multiple of those numbers?

Yes. It's a multiple of each of them.

### Is a factor the product of any two whole numbers?

No, the factors are the whole numbers. The product is the multiple.

A product.

### 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.

### When the greatest common factor is 1 is the least common multiple of these numbers always the product of the numbers?

Yes - if two numbers share no common factors (besides 1) the least common multiple will be the product of the numbers.

yes

### What is the least common multiple of 14 and 70?

Since 70 is a multiple of 14, it is the least common multiple. Or, you can determine it as you would any pair of numbers. The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 14 and 70 is 14. Therefore, the least common multiple 14 x 70 &divide; 14 = 70.