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Answer :
To find the least common multiple (LCM) of 70, 60, and 50, we can follow a step-by-step approach:
1. List the prime factors of each number:
- 70 = 2 × 5 × 7
- 60 = 2² × 3 × 5
- 50 = 2 × 5²
2. Identify the highest power of each prime number present in the factorizations:
- Prime number 2: The highest power is 2² (from 60).
- Prime number 3: The highest power is 3 (from 60).
- Prime number 5: The highest power is 5² (from 50).
- Prime number 7: The highest power is 7 (from 70).
3. Multiply these highest powers together to get the LCM:
[tex]\[
\text{LCM} = 2² × 3 × 5² × 7
\][/tex]
4. Calculate the product:
- First, calculate [tex]\(2² = 4\)[/tex].
- Then, multiply by 3: [tex]\(4 × 3 = 12\)[/tex].
- Next, multiply by [tex]\(5² = 25\)[/tex]: [tex]\(12 × 25 = 300\)[/tex].
- Finally, multiply by 7: [tex]\(300 × 7 = 2100\)[/tex].
The least common multiple of 70, 60, and 50 is 2,100.
1. List the prime factors of each number:
- 70 = 2 × 5 × 7
- 60 = 2² × 3 × 5
- 50 = 2 × 5²
2. Identify the highest power of each prime number present in the factorizations:
- Prime number 2: The highest power is 2² (from 60).
- Prime number 3: The highest power is 3 (from 60).
- Prime number 5: The highest power is 5² (from 50).
- Prime number 7: The highest power is 7 (from 70).
3. Multiply these highest powers together to get the LCM:
[tex]\[
\text{LCM} = 2² × 3 × 5² × 7
\][/tex]
4. Calculate the product:
- First, calculate [tex]\(2² = 4\)[/tex].
- Then, multiply by 3: [tex]\(4 × 3 = 12\)[/tex].
- Next, multiply by [tex]\(5² = 25\)[/tex]: [tex]\(12 × 25 = 300\)[/tex].
- Finally, multiply by 7: [tex]\(300 × 7 = 2100\)[/tex].
The least common multiple of 70, 60, and 50 is 2,100.
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