What Is the Other Number If HCF Is 33 and LCM Is 264?

  • Thread starter chwala
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In summary, this problem is asking for a problem that does not exist. There is no way to solve this problem using the given information.
  • #1
chwala
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Homework Statement
see attached.
Relevant Equations
lcm and hcf
This is the problem,

1632226210016.png


ok, one of the numbers is ##66= 2×3×11## we are told that the hcf = ##33=3×11## therefore, ##11 and 3## would constitute part of the other unknown number, also lcm {264] = {2×2×2×3×11}
the possible value for the other term would be ##{3×11} ## times factors of ##2^n## where, 1≤n≤3
we do not have a solution in the given options.
 
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  • #2
chwala said:
Homework Statement:: see attached.
Relevant Equations:: lcm and hcf

This is the problem,

View attachment 289435

ok, one of the numbers is ##66= 2×3×11## we are told that the hcf = ##33=3×11## therefore, ##11 and 3## would constitute part of the other unknown number, also lcm {264] = {2×2×2×3×11}
the possible value for the other term would be ##{3×11} ## times factors of ##2^n## where, 1≤n≤3
we do not have a solution in the given options.
Where are you getting these crazy problems?
 
  • #3
🤣🤣🤣 these are crazy guys...got this worksheet from Google...lol
 
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  • #4
isnt theee product of two numbers equal to the product of their LCM and HCF?
 
  • #5
mathwonk said:
isnt theee product of two numbers equal to the product of their LCM and HCF?
This may be true but how does it work for this case?
the product of the lcm and hcf is equal to ##8712##, given that the other number is ##66## then it follows that the other unknown number is ##132## but the lcm ##(66,132)=132## and not ##264## as required...and further the hcf of these two numbers is ##66## ...that's why we concluded that it was a crazy question...
 
  • #6
hmmmmm. i think i see your question is not what the answer is, i.e. apparently 33 and 264, but why this answer 264 does not appear in the choices.?
 
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  • #7
mathwonk said:
hmmmmm. i think i see your question is not what the answer is, i.e. apparently 33 and 264, but why this answer 264 does not appear in the choices.?
Not only that...we are informed that ...first number divided by ##2## quotient is ##33##... the first number can only be ##66##. The question is/was wrongly framed.
 
  • #8
ok; i assumed " completely divided by 2" could just mean after dividing out as many powers of 2 as possible, which might be none. but errors are not so hard to find in math. my own works are littered with them. in fact i once refereed a booklet issued by the local school district, or even the state, intended to help high school math teachers prepare for a certification exam, and it had some howlers. good work finding these.
 
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Related to What Is the Other Number If HCF Is 33 and LCM Is 264?

1. What is the difference between HCF and LCM?

The HCF (Highest Common Factor) is the largest number that divides evenly into two or more numbers. The LCM (Lowest Common Multiple) is the smallest number that is a multiple of two or more numbers. In other words, the HCF is the largest shared factor between two or more numbers, while the LCM is the smallest shared multiple.

2. How do you find the HCF and LCM of two numbers?

To find the HCF of two numbers, you can use the prime factorization method or the division method. To find the LCM, you can use the prime factorization method, the division method, or the LCM formula. The LCM formula is LCM = (a*b)/HCF, where a and b are the two numbers.

3. Can you give an example of a HCF and LCM problem?

Sure, let's say we want to find the HCF and LCM of 12 and 18. The prime factorization of 12 is 2*2*3 and the prime factorization of 18 is 2*3*3. The HCF is the product of the common prime factors, which in this case is 2*3 = 6. To find the LCM, we can use the LCM formula: LCM = (12*18)/6 = 36. Therefore, the HCF of 12 and 18 is 6 and the LCM is 36.

4. Why is finding the HCF and LCM important?

Finding the HCF and LCM is important in many mathematical applications, such as simplifying fractions, finding equivalent fractions, and solving word problems involving multiple numbers. It also helps in understanding the relationship between numbers and their factors and multiples.

5. Is there a shortcut for finding the HCF and LCM?

Yes, there are a few shortcuts that can be used to find the HCF and LCM of two or more numbers. One shortcut is to list the multiples of each number and find the smallest shared multiple for the LCM. Another shortcut is to use the "cake method" where you divide each number by the HCF and multiply the quotients to find the LCM. However, it is important to understand the concepts behind HCF and LCM and not solely rely on shortcuts.

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