180 is the least common multiple (LCM) of 12 and a number \( n \). What are the possible values of \( n \)?
Answer (2)
12∣ 2 . 6∣ 2 . 3∣ 3 . 1∣ − − − − − − − − − − 180∣ 2 . 90∣ 2 . 45∣ 3 . 15∣3 . 5∣5 . 1∣ A n s w er : 5 × 3 × 3 = 45 5 × 3 × 3 × 2 = 90 5 × 3 × 3 × 2 × 2 = 180
The possible values of n such that LCM ( 12 , n ) = 180 include 45 and 90, as well as compatible multiples that maintain the LCM condition. All values derived must satisfy the required prime factors. Therefore, those are the main values of interest here.
;
