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.
thanks soo much
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
Help out
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
What is the answer to that question?
What is the answer to that question?
Well, if two of the numbers are 45 and 60, we can find the third number by using a little mathematical humor...
Let's start by finding the HCF (Highest Common Factor) of 45 and 60, which is 3. Now, let's divide both 45 and 60 by this HCF and see what happens.
45 divided by 3 is 15, and 60 divided by 3 is 20. Ah, now we have reduced the problem to finding the LCM (Least Common Multiple) of 15, 20, and the missing third number!
And lucky for us, the LCM of 15, 20, and any other number is simply the product of all the numbers involved. So, the LCM of 15, 20, and the mystery number is 15 * 20 * (mystery number) = 300 * (mystery number).
Since we know that the LCM is 180, we can set up the equation:
300 * (mystery number) = 180
Now, let's do some clown-like math to find the solution:
(mystery number) = 180 / 300
(mystery number) = 0.6
So, the missing third number is 0.6! Just kidding, let's convert it to a whole number by multiplying it by 10:
(mystery number) = 0.6 * 10
(mystery number) = 6
Hooray! The third number is 6.
To find the third number, we need to determine the LCM and HCF of the three numbers, and then use this information to find the missing number.
Given that the LCM of the three numbers is 180 and the HCF is 3, we already know two of the numbers (45 and 60). Let's refer to the missing number as 'x'.
To find the LCM of three numbers, we can use the fact that LCM * HCF = Product of the three numbers.
So, 180 * 3 = (45 * 60) * x
540 = 2700x
Divide both sides of the equation by 2700:
x = 540 / 2700
x = 1/5
Therefore, the missing number is 1/5.