What is the least common multiple (LCM) of 15 and 7?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 15 and 7. To find the LCM, we can use the method of prime factorization or the formula LCM(a, b) = (a * b) / GCD(a, b), where GCD is the greatest common divisor of the two numbers.
Answer
$105$
Answer for screen readers
The least common multiple (LCM) of 15 and 7 is $105$.
Steps to Solve
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Identify the numbers We need to find the least common multiple (LCM) of the numbers 15 and 7.
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Calculate the GCD First, we find the greatest common divisor (GCD) of 15 and 7. Since 15 and 7 don’t have any common factors other than 1, we have: $$ \text{GCD}(15, 7) = 1 $$
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Use the LCM formula Now we can use the formula for LCM: $$ \text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)} $$ Substituting in our values, we have: $$ \text{LCM}(15, 7) = \frac{15 \times 7}{1} $$
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Perform the multiplication Now, compute the product of 15 and 7: $$ 15 \times 7 = 105 $$
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Final calculation Finally, since we calculated the GCD to be 1, the LCM is: $$ \text{LCM}(15, 7) = \frac{105}{1} = 105 $$
The least common multiple (LCM) of 15 and 7 is $105$.
More Information
The least common multiple (LCM) can be thought of as the smallest number that is a multiple of both original numbers. In this case, 105 is the smallest number that can be divided by both 15 and 7 without any remainder.
Tips
- Confusing LCM with GCD: Remember that LCM is about finding a common multiple, while GCD is about finding a common factor.
- Incorrect multiplication or division: Double-check your calculations to ensure accuracy.
