What is the LCM of 7 and 5?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 7 and 5. This is a fundamental math concept where we seek the smallest positive integer that is divisible by both numbers. To find the LCM, we can multiply the two numbers together since they are both prime and have no other common factors.
Answer
The least common multiple (LCM) of 7 and 5 is $35$.
Answer for screen readers
The least common multiple (LCM) of 7 and 5 is $35$.
Steps to Solve
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Identify the numbers We are given two numbers: 7 and 5.
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Check if the numbers are prime Both 7 and 5 are prime numbers, meaning they have no divisors other than 1 and themselves.
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Calculate the LCM Since both numbers are prime and have no common factors, we can find the LCM by multiplying the two numbers together:
$$ \text{LCM}(7, 5) = 7 \times 5 $$
- Perform the multiplication Now we perform the multiplication:
$$ 7 \times 5 = 35 $$
- State the LCM Thus, the least common multiple of 7 and 5 is:
$$ \text{LCM}(7, 5) = 35 $$
The least common multiple (LCM) of 7 and 5 is $35$.
More Information
The least common multiple (LCM) is a crucial concept in number theory. In this case, since both numbers are prime, their LCM is simply their product. This means the smallest common multiple of 7 and 5 is 35.
Tips
- A common mistake is to confuse the least common multiple with the greatest common divisor (gcd). The LCM is the smallest positive integer that is divisible by both numbers, while the gcd is the largest.
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