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what is the LCM of the following numbers. 
1. 20 and 50
2. 18 and 24
3.12 and 16
4. 21 and45
5. 8 and 12

Sagot :

Riza1idn
[tex]\\\\LCM \ stands \ for \ Lowest \ Common \ Multiple.\\ \ LCM \ is \ the \ smallest \ number \ that \ is \ a \ multiple \ of \ both \ {\color{Red} a} \ and \ {\color{Red} b}.[/tex]

[tex]1)\\\\ The \ LCM \ of \ 20 \ and \ 50 \\ \\Multiples \ of \ 20 \ are: \ \ 20, \ 40, \ 60, \ 80, \ \,[100], \ 120, \ 140\ \ and \ so \ on \\Multiples \ of \ 50 \ are: 50, \ [ 100 ] , \ 150, \ 200, \ 250, \ 300\ and \ so \ on\\\\Now \ check \ for \ the \ common \ multiples.\\ Only \ 100 \ is \ the \ common \ multiple \ and \ the \ least \ available \ common \ multiple.\\\\ Answer : \ \ LCM \ of \ 20 \ and \ 50 \ = \ 100.[/tex]

[tex]2)\\\\The \ LCM \ of \ 18\ and \ 24 \\ \\Multiples \ of \ 18 \ are: \ \ 18, \ 36, \ 54, \ [72], \ 90,\ 108 \ and \ so \ on \\Multiples \ of \ 24 \ are: 24, \ 48, \ [72] , \ 96, \ 120\ and \ so \ on\\\\Now \ check \ for \ the \ common \ multiples.\\ Only \ 72 \ is \ the \ common \ multiple \ and \ the \ least \ available \ common \ multiple.\\\\ Answer : \ \ LCM \ of \ 18 \ and \ 24 \ = \ 72 .[/tex]

[tex]3)\\\\The \ LCM \ of \ 12\ and \ 16 \\ \\Multiples \ of \ 12 \ are: \ \ 12, \ 24, \ 36, \ [48] , \ 60,\ 72 \ and \ so \ on \\Multiples \ of \ 16 \ are: 16, \ 32, \ [48] , \ 64, \ 80\ and \ so \ on\\\\Now \ check \ for \ the \ common \ multiples.\\ Only \ 48 \ is \ the \ common \ multiple \ and \ the \ least \ available \ common \ multiple.\\\\ Answer : \ \ LCM \ of \ 12\ and \ 16 \ = \ 48 .[/tex]

[tex]4)\\\\The \ LCM \ of \ 21\ and \ 45\\ \\ Multiples \ of \ 21 \ are: \ \ 21,\ 42, \ 63, \ 84, \ 105,\ 126,\ 147, \ 168, \ 189, \ 210, \\231, \ 252, \ 273, \ 294, \ [ 315] , \ and \ so \ on \\Multiples \ of \ 45 \ are:45, \ 90, \ 135, \ 64, \ 225,\ 270, \ [ 315] , \ and \ so \ on[/tex]

[tex]Now \ check \ for \ the \ common \ multiples.\\ Only \ 315 \ is \ the \ common \ multiple \ and \ the \ least \ available \ common \ multiple.\\\\ Answer : \ \ LCM \ of \ 21 \ and \ 45 \ = \ 315 .[/tex]
 
[tex]5) \\\\\The \ LCM \ of \ 8 \ and \ 12 \\ \\Multiples \ of \ 8\ are: \ \ 8,\ 16, \ 24, \ 32, \ 40,\ [48],\ 56, \ 64, \ and \ so \ on \\Multiples \ of \ 12 \ are:12, \ 24, \ 36, \ [48], \ 60,\ 72, \ and \ so \ on\\\\Now \ check \ for \ the \ common \ multiples.\\ Only \ 48 \ is \ the \ common \ multiple \ and \ the \ least \ available \ common \ multiple.\\\\ Answer : \ \ LCM \ of \ 8 \ and \ 12 \ = \ 48 .[/tex]