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How do you use prime factorization to find the least common multiple of 75 and 45?

Answer 1

Autumn Arnold

LCM is #225#

Initially, determine the two numbers' prime factors, which are as follows:

#75=color(red)(3xx5)xx5# and

#45=3xxcolor(red)(3xx5)#

Now make a list of every common factor—we've already highlighted them in red above.

What is now required in order to write the Least Common Multiple (LCM) is

should list the common factors first, followed by the uncommon ones.

Hence #LCM=color(red)(3xx5)xx5xx3=225#

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Answer 2

Zoe Adams

To find the least common multiple (LCM) of 75 and 45 using prime factorization:

Prime factorize both numbers:
- Prime factorization of 75: 3 × 5 × 5
- Prime factorization of 45: 3 × 3 × 5
Identify the highest power of each prime factor in the prime factorizations:
- Highest power of 3: 3²
- Highest power of 5: 5²
Multiply these highest powers together to get the LCM: LCM = 3² × 5² = 225

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.