Question

the product of two numbers whose lcm is 120 is 720 which of this could be one of the numbers

Answer 1

Given:

The product and LCM of the two numbers are 720 and 120 respectively.

To Find:

The possible numbers that satisfy the above condition.

Solution:

The given problem can be solved by using the concepts of Least Common Multiple.

1. It is mentioned that the product and LCM are 720, 120 respectively.

2. The Least Common Multiple of two numbers is defined as the Common multiple between two numbers which is the least value among the other common multiples. For Example, The LCM of 2 and 4 is 4 as 4 is the Least Common multiple, 8,12,16, and so on are the common multiples but 4 is the least.

3. 720 can be expressed as a multiple of two numbers as the following cases,

= > 1 x 720, 2 x 360, 3 x 240, 4 x 180, 5 x 145, 6 x 120, 8 x 90, 10 x 72, 12 x 60, 15 x 48, 16 x 45, 18 x 40, 20 x 36, 24 x 30.

= > The LCM of 1,720 is 720, 2,360 is 360, 3,240 is 240, 4,180 is 180, 5,145 is 145, 6,120 is 120, 8,90 is 360, 10,72 is 360, 15, 48 240, 16,45 is 720, 18,40 is 360, 20,36 is 180, and 24,30 is 240.

= > Of the mentioned LCM Values the LCM of 6,120 is 120 which is same as the given value. Hence the possible 6, 120 whose product is also 720.

Therefore, the possible values of the numbers with product 720, lcm 120 is 6,120.

Answer 2

The product of two numbers whose lcm is 120 is 720 then 6 , 24 , 30 or 120 can be one of the numbers:

Given:

• Product of two numbers is 720
• LCM = 120

To Find:

• One of the possible number

Solution:

Use Formula

Product of Two numbers (a , b) = HCF (a , b) * LCM ( a, b)

Step 1:

Substitute given values and find HCF

720 = HCF * 120

=> HCF = 6

Step 2:

As HCF is 6 hence Assume that two numbers are

6x , 6y

where x and y are co prime

Step 3:

Equate product of number with 720

6x * 6y = 720

=> x * y  = 20

Step 4:

Find Possible pair of (x , y)

(1 , 20) , (2 , 10) , ( 4 , 5)  

(2 , 10) are not co prime . Hence not possible

So possible pair of  numbers  is

(6 , 120)  and ( 24 , 30)

One Number can be  Any one of the following

6 , 24 , 30 or 120