# -c5.LCM and Prime Factorization of A,B,C

• MHB
• karush
In summary, the least common multiple of A, B, and C is 2(3^2)(5^9)(7)(11)(13^3)(23^8). This can be found by taking the product of all the common and non-common prime factors in the given sets of A, B, and C. The prime factorization of the least common multiple is 2^2(3^2)(5^9)(7)(11)(13^3)(23^8).
karush
Gold Member
MHB
Build the least common multiple of A, B, and C
Then write the prime factorization of the least common multiple of A, B, and C.
$A = 2 \cdot 3^2 \cdot 7 \cdot 13 \cdot 23^8$
$B = 2 3^5 \cdot 5^9 \cdot 13$
$C = 2 \cdot 5 \cdot 11^8 \cdot 13^3$
$\boxed{?}$

ok this only has a single answer

definition: Prime factorization is a way of expressing a number as a product of its prime factors.
A prime number is a number that has exactly two factors, 1 and the number itself.

so is our first step $A\cdot B \cdot C$

Last edited:
No, of course not. ABC would be a "common multiple" of A, B, and C but the "LEAST common multiple" only if all three numbers are relatively prime which is not the case here. I see that A and C have a factor of 2 so the LCM will have a factor of 2. A has a factor of $$\displaystyle 3^2$$ so the LCM will have $$\displaystyle 3^2$$ as factor. B has a factor of $$\displaystyle 5^9$$ and C has a factor of 5 so the LCM will have $$\displaystyle 5^9$$ as a factor. B has 7 as a factor so the LCM has 7 as a factor. C has a factor of 11 so the LCM will have 11 as a factor. A and B have 13 as a factor and C has $$\displaystyle 13^3$$ as a factor so the LCM will have $$\displaystyle 13^3$$ as a factor. A has $$\displaystyle 23^8$$ as a factor and $$\displaystyle 23^5$$ so the LCM has $$\displaystyle 23^8$$ as a factor.

The least common multiple of A, B, and C is $$\displaystyle 2(3^2)(5^9)(7)(11)(13^3)(23^8)$$.

sorry I just noticed that $B=2\cdot 3^5\cdot 5^9 \cdot 13$
probably will change every thing
I should just OP the screenshots

You still use the same principal:
for the greatest common factor of a set of numbers, take the product of all primes to the smallest power in the given set and for the least common multiple take the product of all primes to the highest power.

## 1. What is the LCM of A, B, and C?

The LCM (Least Common Multiple) of A, B, and C is the smallest positive integer that is divisible by all three numbers without any remainder.

## 2. How do you find the LCM of A, B, and C?

The LCM can be found by first finding the prime factorization of each number. Then, the LCM is the product of the highest powers of each prime factor that appear in any of the numbers.

## 3. What is prime factorization?

Prime factorization is the process of breaking down a number into its prime factors, which are the numbers that can only be divided by 1 and themselves. This is done by repeatedly dividing the number by its smallest prime factor until the result is 1.

## 4. Why is prime factorization important in finding the LCM?

Prime factorization is important in finding the LCM because it allows us to identify the common factors among the numbers. By finding the highest powers of these common factors, we can determine the LCM.

## 5. Can you use the LCM to find the GCF (Greatest Common Factor) of A, B, and C?

Yes, the GCF can be found by dividing the LCM of A, B, and C by the product of the numbers. This will give us the highest common factor among the numbers.

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