What is the LCM (Least Common Multiple) of the following pairs of numbers?
1. 4 and 14
2. 12 and 21
3. 16 and 12
4. 25 and 30
5. 40 and 50
6. 18 and 24
Answer (3)
12∣2 . 6∣2 . 3∣3 . 1∣ 12 = 2 × 2 × 3 21∣3 . 7∣7 . 1∣ 21 = 3 × 7 L CM ( 12 ; 21 ) = 3 × 2 × 2 × 7 = 84
16∣2 . 8∣2 . 4∣2 . 2∣2 . 1∣ 16 = 2 × 2 × 2 × 2 12∣2 . 6∣2 . 3∣3 . 1∣ 12 = 2 × 2 × 3 L CM ( 16 ; 12 ) = 2 × 2 × 2 × 2 × 3 = 48
25∣5 . 5∣5 . 1∣ 25 = 5 × 5 30∣2 15∣3 . 5∣5 . 1∣ 30 = 2 × 3 × 5 L CM ( 25 ; 30 ) = 5 × 5 × 2 × 3 = 150
40∣2 20∣2 10∣2 . 5∣5 . 1∣ 40 = 2 × 2 × 2 × 5 50∣2 25∣5 . 5∣5 . 1∣ 50 = 2 × 5 × 5 L CM ( 40 ; 50 ) = 2 × 5 × 2 × 2 × 5 = 200
18∣2 . 9∣3 . 3∣3 . 1∣ 18 = 2 × 3 × 3 24∣2 12∣2 . 6∣2 . 3∣3 . 1∣ 24 = 2 × 2 × 2 × 3 L CM ( 18 ; 24 ) = 2 × 3 × 3 × 2 × 2 = 72
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.
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
40: 40, 80, 120, 160, 200, 240, 280, 320, 360... 50: 50, 100, 150, 200, 250, 300, 350... Answer: 200
18:18, 36, 54, 72, 90, 108, 126 24: 24, 48, 72, 96, 120 Answer:72
The LCM values for the given pairs are: 28 (4 and 14), 84 (12 and 21), 48 (16 and 12), 150 (25 and 30), 200 (40 and 50), and 72 (18 and 24).
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