A number L is called a common multiple of m and n if both mand n divide L. The smallest such L is called the least common multiple of m and n and is denoted by LCMCm,n). For example, LCM (3,7) 21 ond LCM (12, 66) = 132 aj Find the following least common multiplies. (LCM (8,12) ciis LCM (20,30) (iii) LCM (51,68) LCM (23,48) b.) For each of the LCM's that the LCM's that you computed in ca), compare the value of LCM (min) to the values of min and god. (min). Try" find a relationship. that the relationship G Give art arguement proving is correct for all mand' n. you found ol. Use result in cb) to compute LCM (301337, 307829) your e.) Soppose that gid (min)- 18 and LCM (min) = 720. Find m and n. Is there more than possibility? If so, find all of them.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
D,e
A number L is called
common
mand in divide L. The smallest such L is called the least common
multiple of m and n if both
multiple of m ond n and is denoted by LCMCm, n). For example,
LCM (3,7) 21 ond LCM (12, 66) = 132
aj Find the following least common multiplies
the
(LCM (8,12) cii) LCM (20,30) (iii) LCM (51,68) LCM (23, 18)
b. For each of the LCM's that
you computed in ca), compare
value of LCM Cmin) to the values of min and god (min). Try
find a relationship.
to
that the relationship you found
G) bive an arguement proving
correct for all mand' n.
is
result in cb) to compute LCM (301337, 307829)
ol. Use
your
e.) Soppose that gcd (m,n) = 18 and LCM (m,n) = 720 - Find m and
n. Is there more than possibility? If so, find all of them.
Transcribed Image Text:A number L is called common mand in divide L. The smallest such L is called the least common multiple of m and n if both multiple of m ond n and is denoted by LCMCm, n). For example, LCM (3,7) 21 ond LCM (12, 66) = 132 aj Find the following least common multiplies the (LCM (8,12) cii) LCM (20,30) (iii) LCM (51,68) LCM (23, 18) b. For each of the LCM's that you computed in ca), compare value of LCM Cmin) to the values of min and god (min). Try find a relationship. to that the relationship you found G) bive an arguement proving correct for all mand' n. is result in cb) to compute LCM (301337, 307829) ol. Use your e.) Soppose that gcd (m,n) = 18 and LCM (m,n) = 720 - Find m and n. Is there more than possibility? If so, find all of them.
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