Find the L.C.M. of the numbers in the table given below: Numbers The multiples of the numbers L.C.M. 3 , 5 , 6

Here, we have Numbers The multiples of the numbers L.C.M. 3 , 5 , 6 Given numbers are 3 , 5 , 6 . L.C.M. is the least common multiple of two or more numbers which is a multiple of all the numbers. Thus, multiple of given numbers are: Multiples of 3 = 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 , 30 Multiples of 5 = 5 , 10 , 15 , 20 , 25 , 30 Multiple of 6 = 6 , 12 , 18 , 24 , 30 So, we can see that 30 is least multiple which is common in all the numbers. Thus, the L.C.M. of 3 , 5 , 6 is 30 . Therefore, the table is: Numbers The multiples of the numbers L.C.M. 3 , 5 , 6 Multiples of 3 = 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 , 30 Multiples of 5 = 5 , 10 , 15 , 20 , 25 , 30 Multiples of 6 = 6 , 12 , 18 , 24 , 30 30

Find the L.C.M. of the numbers in the table given below: Numbers The multiples of the numbers L.C.M. 4 , 9 , 12

Here, we have Numbers The multiples of the numbers L.C.M. 4 , 9 , 12 Given numbers are 4 , 9 , 12 . L.C.M. is the least common multiple of two or more numbers which is a multiple of all the numbers. Thus, multiple of given numbers are: Multiples of 4 = 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , 36 Multiples of 9 = 9 , 18 , 27 , 36 Multiple of 12 = 12 , 24 , 36 So, we can see that 36 is least multiple which is common in all the numbers. Thus, the L.C.M. of 4 , 9 , 12 is 36 . Therefore, the table is: Numbers The multiples of the numbers L.C.M. 4 , 9 , 12 Multiples of 4 = 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 , 36 Multiples of 9 = 9 , 18 , 27 , 36 Multiples of 12 = 12 , 24 , 36 36

Verify, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) by finding the HCF and LCM of the numbers given below, 4 , 9

Given numbers 4 , 9 To verify Product of two numbers = LCM ( a , b ) × HCF ( a , b ) Using prime factorization method, 4 = 2 × 2 9 = 3 × 3 LCM ( a , b ) = 2 × 2 × 3 × 3 = 36 HCF ( a , b ) = 1 Product of two numbers = 4 × 9 = 36 LCM ( a , b ) × HCF ( a , b ) = 36 × 1 = 36 Thus, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) is verified.

Verify, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) by finding the HCF and LCM of the numbers given below, 30 , 36

Given numbers 30 , 36 To verify Product of two numbers = LCM ( a , b ) × HCF ( a , b ) Using prime factorization method, 30 = 2 × 5 × 3 36 = 3 × 3 × 2 × 2 LCM ( a , b ) = 2 × 2 × 3 × 3 × 5 = 180 HCF ( a , b ) = 3 × 2 = 6 Product of two numbers = 30 × 36 = 1080 LCM ( a , b ) × HCF ( a , b ) = 180 × 6 = 1080 Thus, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) is verified.

Verify, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) by finding the HCF and LCM of the numbers given below, 42 , 48

Given numbers 42 , 48 To verify Product of two numbers = LCM ( a , b ) × HCF ( a , b ) Using prime factorization method, 42 = 2 × 3 × 7 48 = 2 × 2 × 2 × 2 × 3 LCM ( a , b ) = 2 × 3 × 2 × 2 × 2 × 7 = 336 HCF ( a , b ) = 2 × 3 = 6 Product of two numbers = 42 × 48 = 2016 LCM ( a , b ) × HCF ( a , b ) = 336 × 6 = 2016 Thus, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) is verified.

Verify, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) by finding the HCF and LCM of the numbers given below, 108 , 18

Given numbers 108 , 18 To verify Product of two numbers = LCM ( a , b ) × HCF ( a , b ) Using prime factorization method, 108 = 2 × 2 × 3 × 3 × 3 18 = 3 × 3 × 2 LCM ( a , b ) = 2 × 2 × 3 × 3 × 3 = 108 HCF ( a , b ) = 18 Product of two numbers = 108 × 18 = 1944 LCM ( a , b ) × HCF ( a , b ) = 108 × 18 = 1944 Thus, Product of two numbers = LCM ( a , b ) × HCF ( a , b ) is verified.