
3 and 16 2 and 4 4 and 8 4 and 16
 LCM by using prime factorization
 LCM by using repeated division
 LCM by using multiple
Expert Answer
The LCM for each pair is calculated as follows The LCM of $3$ and $16$ will be: \[3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, …\] \[16 = 16, 32, 48, …\] Common Multiple is $48$. As it is the smallest common multiple, hence: \[LCM = 48\] The LCM of $2$ and $4$ will be: \[2 = 2, 4, 6, 12, …\] \[4 = 4, 8, 12, …\] Common Multiples are $4,8, …$. As the smallest common multiple is $4$, hence \[LCM = 4\] The LCM of $4$ and $8$ will be: \[4 = 4, 8, 12, 16, 20, 24, …\] \[8 = 8, 16, 24, …\] Common Multiples are $8,16, …$. As the smallest common multiple is $8$, hence \[LCM = 8\] The LCM of $4$ and $16$ will be: \[4 = 4, 8, 12, 16, 20, 24, 28, 32, …\] \[16 = 16, 32, …\] Common Multiples are $16, 32, …$. As the smallest common multiple is $16$, hence \[LCM = 16\]Numerical Results:
So the required pair of numbers for which the LCM is $16$ is $4$ and $16$Example:
Find out which of the following pairs has the LCM of $24$. $a)$ $3$ and $8$ $b)$ $2$ and $12$ $c)$ $6$ and $4$ $d)$ $4$ and $12$Solution:
The LCM of $3$ and $8$ will be: \[3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, …\] \[8 = 8, 16, 24, 32, 40, 48, …\] \[LCM = 24\] The LCM of $2$ and $12$ will be: \[2 = 2 ,4, 6, …\] \[12 = 12, 24, 36, 48, 60, 72, …\] \[LCM = 12\] The LCM of $4$ and $6$ will be: \[4 = 4, 8, 12, 16, 20, …\] \[6 = 6, 12, 18, 24, …\] \[LCM = 12\] The LCM of $4$ and $12$ will be: \[4 = 4, 8, 12, 16, 20, …\] \[12 = 12, 24, 36, 48, 60, 72, …\] \[LCM = 12\] So the required pair is $3$ and $8$. Image/Mathematical drawings are created in Geogebra.Previous Question < > Next Question
5/5  (11 votes)