Three whole number have their LCM as 180 and their HCF equal to 3. Two of the numbers are 45 and 60. Find the third number.
The HCF of 108,189 and a certain number is 27 and their LCM is 3780. Find the value of the third number.
The LCM of 132,330 and a certain number is 1980 and their HCF is 66. Find the value of the number.
45 = 3*3*5
60 = 2*2*3*5
The LCM of those two alone would be 2*2*3*3*5 = 180
since the 3rd number also has a common factor of 3,
the third number could be 3
The 3rd number could be more than the above choice,
e.g. it could have been 6 , 15, 9, 12, or 18
Can you think of any others?
What would be your criteria ?
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The HCF and the LCM of 108,189 and a third number is 27 and 3780 respectively. The third number can be
To find the third number, we can use the fact that the LCM (Least Common Multiple) of three numbers can be found by multiplying the three numbers together and then dividing by their HCF (Highest Common Factor).
Given that the two numbers are 45 and 60, we need to find the third number.
Step 1: Find the LCM of the given two numbers.
The LCM of 45 and 60 can be found by dividing their product by their HCF: 180 / 3 = 60.
Step 2: Multiply the LCM by the HCF of the three numbers.
Since the LCM of the three numbers is given as 180 and the HCF is given as 3, we can write the equation as:
180 = 60 * 3 * third number
Step 3: Solve for the third number.
Divide both sides of the equation by 180 / (60 * 3) to get the value of the third number:
third number = 180 / (60 * 3) = 1
Therefore, the third number is 1.