Answer:
[tex]LCM(1,2,12,30,84,165)=2^2*3*5*7*11*1=4620[/tex]
Step-by-step explanation:
To find the LCM of 1,2,12,30,84,165 you must first find the prime factors of 12,30,84 and 165
12| 2 30| 2 84| 2 165| 3
6 | 2 15 | 3 42| 2 55 | 5
3 | 3 5 | 5 21 | 3 11 | 11
1 1 7 | 7 1
1
[tex]12=2^2*3[/tex] [tex]30=2*3*5[/tex] [tex]84=2^2*3*7[/tex] [tex]165=3*5*11[/tex]
Now we look for common and uncommon factors with their greatest exponent
LCM(1,2,12,30,84,165)
Common factors with their greatest exponent: [tex]2^2*3*5[/tex]
Uncommon factors with their greatest exponent: [tex]7*11*1[/tex]
[tex]LCM(1,2,12,30,84,165)=2^2*3*5*7*11*1=4620[/tex]
