Lcm and Hcf question

[Kirti]

Hi please can you help me with this question;

The LCM of a and b is 2^5 × 3^3 and the HCF of a and b is 2^2 × 3^2.

Given that a = 2^2 × 3^3 , find the value of b ?

 

[Deleted member 4993]

Hi please can you help me with this question;

The LCM of a and b is 2^5 × 3^3 and the HCF of a and b is 2^2 × 3^2.

Given that a = 2^2 × 3^3 , find the value of b ?

Hint:

The product of the two numbers is the product of the LCM and the HCF.

 

[Kirti]

Thank you , Is this right , then.

b = 2^5 × 3^2 ?

How can i confirm this is right please ?

 

[pka]

The LCM of a and b is 2^5 × 3^3 and the HCF of a and b is 2^2 × 3^2.
Given that a = 2^2 × 3^3 , find the value of b ?

EDIT

Here are the rules: Write each number in prime factor form.
LCM:LCM: List all primes that appear in either number. Then take the highest power of each.
HCF:HCF: List only common primes. Then take the Least power of those.
Did you follow those rules?

Did you follow those rules?

 

[Dr.Peterson]

Hi please can you help me with this question;

The LCM of a and b is 2^5 × 3^3 and the HCF of a and b is 2^2 × 3^2.

Given that a = 2^2 × 3^3 , find the value of b ?

Thank you , Is this right , then.

b = 2^5 × 3^2 ?

How can i confirm this is right please ?

Did you check against the given conditions?

If [MATH]a = 2^2 × 3^3[/MATH] and [MATH]b = 2^5 × 3^2[/MATH], the LCM is [MATH]2^5 × 3^3[/MATH], which is correct; and the HCF is [MATH]2^2 × 3^2[/MATH]. So you're right.

Why did you need to ask?

 

[JeffM]

Here are the rules: Write each number in prime factor form.
\(LCM:\) List all primes that appear in either number. Then take the least power of each.
\(HCF:\) List only common primes. Then take the highest power of those.
Did you follow those rules?

I do not grasp these rules.

Consider 60 = 2^2 * 3 * 5 and 90 = 2 * 3^2 * 5. The least power of each prime is 1, but 2 * 3 * 5 = 30 is not the least common multiple of 60 and 90. In fact 30 is not a multiple of either 60 or 90.

Am I misreading what you wrote?

 

[Kirti]

Did you check against the given conditions?

If [MATH]a = 2^2 × 3^3[/MATH] and [MATH]b = 2^5 × 3^2[/MATH], the LCM is [MATH]2^5 × 3^3[/MATH], which is correct; and the HCF is [MATH]2^2 × 3^2[/MATH]. So you're right.

Why did you need to ask?

 

[Kirti]

I used the first hint and worked it out then got confused as doubted myself when reading the rule about the definition of LCM and HCF.

Basically balamcing the equations if RHS=LHS is equal then we have confidencein solution.

 

[pka]

EDIT

Here are the rules: Write each number in prime factor form.
\(LCM:\) List all primes that appear in either number. Then take the highest power of each.
\(HCF:\) List only common primes. Then take the Least power of those.
Did you follow those rules?

 

[JeffM]

EDIT

I do not believe anyone ever specified an algorithm for these processes at any time in my school career..

 

[Kirti]

It would have been ideal ,

 

[Steven G]

Thank you , Is this right , then.

b = 2^5 × 3^2 ?

How can i confirm this is right please ?

Subhotosh gave you the way to check it! a*b must equal LCM(a,b)*HCF(a,b)

 

[Steven G]

I do not grasp these rules.

Consider 60 = 2^2 * 3 * 5 and 90 = 2 * 3^2 * 5. The least power of each prime is 1, but 2 * 3 * 5 = 30 is not the least common multiple of 60 and 90. In fact 30 is not a multiple of either 60 or 90.

Am I misreading what you wrote?

I am not sure what you are missing here based on your expertise that you constantly show on this website. Please don't be offended if what follows is already obvious to you.

To find the LCM(2^2 * 3 * 5, 2 * 3^2 * 5) you write down all the distinct factors which are 2 and 3. Now between the two numbers (60 and 90) you pick the highest power for each prime to use as the power for each prime. This gives you 2^2*3^2*5=180 as the LCM(60,90).
For the GCF you pick the smallest power for each prime (which might be 0) house as the power.

 

[Dr.Peterson]

JeffM was responding to the erroneous post #4, which was corrected in post #9. Neither explicitly points out that this is a method for finding the LCM and HCF (GCF), not a method for solving the problem as given. It is a method for checking the answer, and can also lead to a way to solve the problem itself by working backward. I say this in case the OP (or JeffM) missed that.