LCM: Prime Factorization Method
Medium difficulty multiple-choice quiz based on the Math Antics Extras video about finding LCM using prime factorization.
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Quiz Questions & Answers
Review every prompt, the correct responses, and helpful context to prep for your own run-through.
Question 1: What is the primary advantage of using the Prime Factorization Method to find the LCM, as described in the video?
It only works for numbers that are already prime
It constructs the LCM from prime factors instead of listing many multiples
It avoids multiplication entirely
It always gives a smaller number than any other method
Question 2: When combining prime factorizations to make the LCM, how should overlapping prime factors be handled?
Include only one copy of each overlapping prime factor
Exclude overlapping primes completely
Double the overlapping primes to be safe
Only use overlapping primes and discard unique ones
Question 3: If two numbers have no common prime factors, what does the video say about their LCM?
The LCM is always their difference
There is no LCM if they share no primes
The LCM is the larger of the two numbers
The LCM equals the product of the two numbers
Question 4: In the example with 12 and 14, which combined prime factors produce the LCM?
12 × 14
2 × 3 × 7
2 × 2 × 3 × 7
2 × 2 × 2 × 3 × 7
Question 5: Why does multiplying the two original numbers always produce a common multiple but not necessarily the LCM?
Because products are only divisible by prime numbers
Because products are never common multiples
Because multiplying both numbers duplicates shared prime factors, possibly making a larger multiple
Because the product removes necessary factors
Question 6: Given 105 = 3×5×7 and 120 = 2×2×2×3×5, which primes must appear (and how many times) in the LCM's factorization?
2×2×2×3×5×7 (three 2s, one 3, one 5, one 7)
2×2×2×3×5 (omit 7)
2×2×3×3×5×7
3×5×7
Question 7: Which mindset or check does the video recommend to ensure the LCM you built is actually the least?
Ensure the result is prime
Check that the result is bigger than both original numbers
Make sure you used only one copy of any prime that appears in both factorizations
Always include at least two copies of every prime