Question

Two numbers are in the ratio 2:3. If their HCF is 18, then what is their LCM? ​

Answer 1

Answer:

Step-by-step explanation:

Given that:

Two numbers ratio = 2:3

HCF of two number = 18

To Find:

LCM of two numbers

Solution:

• Firstly , we assume that the two numbers are 2x and 3x.                                    

• And by taking the HCF of above two number .

• We get that x is the HCF of two number

Now , in Question we have given that HCF is 18.

• So , we take x = 18 .

Now , Solving the Equation We get,

           LCM   =  2 * 3 * x

           LCM   =  6 * 18

           LCM   =   108

So, LCM of the Two number is 108.

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Answer 2

Answer:Required LCM of two numbers is 108.

Explanation:

Given:Two numbers are in the ratio 2:3

          HCF of two numbers is 18.

To find:We have to find the LCM of the two numbers.

Step 1:Let the two numbers are 2x and 3x respectively.

Step 2:The HCF of the two numbers 2x and 3x is x.

∵         The value of HCF IS 18.

∴                           $x=18$

Step 3:Now we can give the numbers as,

                 $2x=2$×$18$$= 36$

and           $3x=3$×$18=54$

Thus the two numbers are 36 and 54 respectively.

Step 4:Now we have to find out the LCM OF 36 AND 54.

                          $LCM=2$×$2$×$3$×$3$×$3$

                          $LCM=4$×$27$

                          $LCM=108$        

Thus,required LCM of two numbers is 108.

What is Least Common Multiple(LCM):The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.It is also known as lowest common multiple

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