Question

the lcm of three numbers is 7920 and their GCD is 12.Two of the numbers are 264using factor notation find the third number if one of its factor is 9

Answer 1

Step-by-step explanation:

The LCM of 3 numbers is 7920 and GCD is 12. Two of the numbers are 48 and 264. Using factors notation, what is the 3rd number if one of its factors is 9?

gcd(a,b,c)=gcd(gcd(a,b),c)

gcd(48,264)=24=23⋅3

48=24⋅3

264=23⋅3⋅11

gcd(24,n)=12⟹n=12o where o is an odd number.

We know 9∣n so it follows that o is a multiple of 3 .

7920=24⋅32⋅5⋅11 .

Ok we have n=22⋅32⋅5=180 as smallest possible value for n but multiplying this result with 11 wouldn’t change it.

Answer 2

Answer:

1980 is the third number

Step-by-step explanation:

2²×3²×5×11=1980