What is the least common multiple of 7 and 8?
Understand the Problem
The question is asking us to calculate the least common multiple (LCM) of the numbers 7 and 8. We can find the LCM by identifying the smallest multiple that both numbers share.
Answer
56
Answer for screen readers
The least common multiple is 56
Steps to Solve
- Determine the prime factors of each number
Identify the prime factors of 7 and 8. Since both are prime numbers, their prime factors are:
$$ 7 = 7 $$ $$ 8 = 2^3 $$
- Identify the highest power of each prime number
Select the highest power of all prime numbers that appear in the prime factorizations of both numbers:
The prime factors are 2 and 7. The highest powers are: $$ 2^3 = 8 $$ $$ 7^1 = 7 $$
- Calculate the LCM by multiplying the highest powers
Multiply the highest powers of the prime factors to find the LCM:
$$ LCM = 2^3 imes 7^1 = 8 imes 7 = 56 $$
The least common multiple is 56
More Information
It can be useful to know that the LCM of two numbers is always at least as large as the largest number.
Tips
A common mistake is not using the highest powers of all prime numbers found in the prime factorizations.
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