find the Lcm of 13 and 20. 2) find the Lcm of 17 and 10.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for finding the Least Common Multiple (LCM):

1) Find the LCM of 13 and 20.

Find the prime factorization of each number.
$13 = 13$ $20 = 2 \times 2 \times 5 = 2^2 \times 5$
Identify all unique prime factors and take the highest power of each.
The unique prime factors are 2, 5, and 13.
The highest power of 2 is $2^2$ .
The highest power of 5 is $5^1$ .
The highest power of 13 is $13^1$ .
Multiply these highest powers together to find the LCM.
$\text{LCM}(13, 20) = 2^2 \times 5 \times 13 = 4 \times 5 \times 13 = 20 \times 13 = 260$
The LCM of 13 and 20 is $\boxed{260}$ .

2) Find the LCM of 17 and 10.
Find the prime factorization of each number.
$17 = 17$ $10 = 2 \times 5$
Identify all unique prime factors and take the highest power of each.
The unique prime factors are 2, 5, and 17.
The highest power of 2 is $2^1$ .
The highest power of 5 is $5^1$ .
The highest power of 17 is $17^1$ .
Multiply these highest powers together to find the LCM.
$\text{LCM}(17, 10) = 2 \times 5 \times 17 = 10 \times 17 = 170$
The LCM of 17 and 10 is $\boxed{170}$ .

Find the Lcm of 13 and 20. 2) find the Lcm of 17 and 10.