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Answer :
To work out the least common multiple (LCM) of 15 and 20, let's follow these steps:
1. Understand Prime Factorization:
- First, we need to find the prime factorization of each number.
- 15 can be expressed as 3 × 5.
- 20 can be expressed as 2 × 2 × 5 (or [tex]\(2^2 × 5\)[/tex]).
2. List All Prime Factors:
- For the LCM, we take the highest power of each prime number that appears in the factorization of the given numbers.
- From 15, we have the prime factors 3 and 5.
- From 20, we have the prime factors 2 and 5.
3. Determine the LCM by Using the Highest Powers:
- For the prime number 2, it appears in the factorization of 20 as [tex]\(2^2\)[/tex]. So, we use [tex]\(2^2\)[/tex].
- For the prime number 3, it appears in the factorization of 15 as [tex]\(3^1\)[/tex]. So, we use [tex]\(3^1\)[/tex].
- For the prime number 5, it appears in both numbers, but the highest power is [tex]\(5^1\)[/tex]. So, we use [tex]\(5^1\)[/tex].
4. Calculate the LCM:
- Multiply the selected prime factors: [tex]\(2^2 × 3^1 × 5^1\)[/tex].
- Compute this step-by-step:
- [tex]\(2^2 = 4\)[/tex]
- [tex]\(4 × 3 = 12\)[/tex]
- [tex]\(12 × 5 = 60\)[/tex]
Therefore, the least common multiple (LCM) of 15 and 20 is 60.
1. Understand Prime Factorization:
- First, we need to find the prime factorization of each number.
- 15 can be expressed as 3 × 5.
- 20 can be expressed as 2 × 2 × 5 (or [tex]\(2^2 × 5\)[/tex]).
2. List All Prime Factors:
- For the LCM, we take the highest power of each prime number that appears in the factorization of the given numbers.
- From 15, we have the prime factors 3 and 5.
- From 20, we have the prime factors 2 and 5.
3. Determine the LCM by Using the Highest Powers:
- For the prime number 2, it appears in the factorization of 20 as [tex]\(2^2\)[/tex]. So, we use [tex]\(2^2\)[/tex].
- For the prime number 3, it appears in the factorization of 15 as [tex]\(3^1\)[/tex]. So, we use [tex]\(3^1\)[/tex].
- For the prime number 5, it appears in both numbers, but the highest power is [tex]\(5^1\)[/tex]. So, we use [tex]\(5^1\)[/tex].
4. Calculate the LCM:
- Multiply the selected prime factors: [tex]\(2^2 × 3^1 × 5^1\)[/tex].
- Compute this step-by-step:
- [tex]\(2^2 = 4\)[/tex]
- [tex]\(4 × 3 = 12\)[/tex]
- [tex]\(12 × 5 = 60\)[/tex]
Therefore, the least common multiple (LCM) of 15 and 20 is 60.
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