Question

three whole numbers have their LCM as 180 and their HCF equal to 3. two of the numbers are 45 and 60. Find the third number.

Answer 1

well,

45 = 3*15 = 3*(3 * 5)
60 = 3*20 = 3*(2^2 5)
180 = 2^2 3^2 5
So, the third number is 3*(3 * 2^2 * 5) = 180

Answer 2

thanks soo much

Answer 3

45=3^2*5
60=2^2*3*5
let the third number =x
x=2^a*2^b

if x=3, x=3
lcm of 3,45 and 60=2^2*3^2*5=180
hcf of 3,45 and 60=3

if x=2*3, x=6
lcm of 6,45 and 60=2^2*3^2*5=180
hcf of 6,45 and 60=3

if x=3^2, x=9
lcm of 9,45 and 60= 2^2*3^2*5=180
hcf of 9,45 and 60=3

if x=2^2*3, x=12
lcm of 12,45 and 60=2^2*3^2*5=180
hcf of 12,45 and 60=3

if x=2*3^2, x=18
lcm of 18,45 and 60=2^2*3^2*5=180
hcf of 18,45 and 60=3

if x=2^2*3^2=36
lcm of 36,45 and 60=2^2*3^2*5=180
hcf of 36=45 and 60=3

hence the third number is either 3,6,9,12,18 or 36

Answer 4

Help out

Answer 5

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