Verified Answer :

elmina247

Basically what you do is list the multiples of your given numbers, and the first number they have in common is your least common multiple.
1) 12: 12, 24, 36, 48, 60, 72, 84, 96, 108...
    21: 21, 42, 63, 84, 105...
Answer: 84

2) 16: 16, 32, 48, 64, 80...
    12: 12, 24, 36, 48, 60, 72, 84, 96, 108...
Answer: 48

3) 25: 25, 50, 75, 100, 125, 150, 175, 200...
    30: 30, 60, 90, 120, 150, 180, 210...
Answer:150

4) 40: 40, 80, 120, 160, 200, 240, 280, 320, 360...
    50: 50, 100, 150, 200, 250, 300, 350...
Answer: 200

5) 18:18, 36, 54, 72, 90, 108, 126
    24: 24, 48, 72, 96, 120
Answer:72

\(12|2\\.\ 6|2\\.\ 3|3\\.\ 1|\\12=2\times2\times\fbox3\\\\21|3\\.\ 7|7\\.\ 1|\\21=\fbox3\times7\\\\LCM(12;\ 21)=\fbox3\times2\times2\times7=84\)


\(16|2\\.\ 8|2\\.\ 4|2\\.\ 2|2\\.\ 1|\\16=\fbox2\times\fbox2\times2\times2\\\\12|2\\.\ 6|2\\.\ 3|3\\.\ 1|\\12=\fbox2\times\fbox2\times3\\\\LCM(16;\ 12)=\fbox2\times\fbox2\times2\times2\times3=48\)


\(25|5\\.\ 5|5\\.\ 1|\\25=\fbox5\times5\\\\30|2\\15|3\\.\ 5|5\\.\ 1|\\30=2\times3\times\fbox5\\\\LCM(25;\ 30)=\fbox5\times5\times2\times3=150\)


\(40|2\\20|2\\10|2\\.\ 5|5\\.\ 1|\\40=\fbox2\times2\times2\times\fbox5\\\\50|2\\25|5\\.\ 5|5\\.\ 1|\\50=\fbox2\times\fbox5\times5\\\\LCM(40;\ 50)=\fbox2\times\fbox5\times2\times2\times5=200\)


\(18|2\\.\ 9|3\\.\ 3|3\\.\ 1|\\18=\fbox2\times\fbox3\times3\\\\24|2\\12|2\\.\ 6|2\\.\ 3|3\\.\ 1|\\24=\fbox2\times2\times2\times\fbox3\\\\LCM(18;\ 24)=\fbox2\times\fbox3\times3\times2\times2=72\)

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