Question

relation between HCF and LCM of class 5th ​

Answer 1

Relation between HCF and LCM

Product of two numbers = Product of their HCF and LCM.

Example

LCM (8, 14) = 56

HCF (8, 14) = 2

LCM (8, 14) × HCF (8, 14) = 56 × 2 = 112

8 × 14 = 112

Hence LCM (8, 14) × HCF (8, 14) = 8 × 14

Least Common Multiple (LCM) of fractions

LCM of fractions

=

LCM of Numerators

HCF of Denominators

=LCM of NumeratorsHCF of Denominators

Example 1: Find out LCM of

1

2

12,

3

8

38,

3

4

34

LCM

=

LCM (1, 3, 3)

HCF (2, 8, 4)

=

3

2

=LCM (1, 3, 3)HCF (2, 8, 4)=32

Example 2: Find out LCM of

2

5

25,

3

10

310

LCM =

LCM (2, 3)

HCF (5, 10)

=

6

5

LCM (2, 3)HCF (5, 10)=65

Highest Common Multiple (HCF) of fractions

HCF of fractions

=

HCF of Numerators

LCM of Denominators

=HCF of NumeratorsLCM of Denominators

Example 1: Find out HCF of

3

5

35,

6

11

611,

9

20

920

HCF

=

HCF (3, 6, 9)

LCM (5, 11, 20)

=

3

220

=HCF (3, 6, 9)LCM (5, 11, 20)=3220

Example 2: Find out HCF of

4

5

45,

2

3

23

HCF =

HCF (4, 2)

LCM (5, 3)

=

2

15

HCF (4, 2)LCM (5, 3)=215

How to calculate LCM and HCF of Decimals

Step 1: Make the same number of decimal places in all the given numbers by suffixing zero(s) in required numbers as needed.

Step 2: Now find the LCM/HCF of these numbers without decimal.

Step 3: Put the decimal point in the result obtained in step 2 leaving as many digits on its right as there are in each of the numbers.

Example: Find the LCM and HCF of .63, 1.05, 2.1

Step 1: Make the same number of decimal places in all the given numbers by suffixing zero(s) in required numbers as needed.

i.e., the numbers can be writtten as .63, 1.05, 2.10

Step 2: Now find the LCM/HCF of these numbers without decimal.

Without decimal, the numbers can be written as 63, 105 and 210 .

LCM (63, 105 and 210) = 630

HCF (63, 105 and 210) = 21

Step 3 : Put the decimal point in the result obtained in step 2 leaving as many digits on its right as there are in each of the numbers.

i.e., here, we need to put decimal point in the result obtained in step 2 leaving two digits on its right.

i.e., the LCM (.63, 1.05, 2.1) = 6.30

HCF (.63, 1.05, 2.1) = .21

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Answer 2

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$\bf\underline\red{Ur-answer-is-here}$

=> Relation between HCF and LCMProduct of two numbers = Product of their HCF and LCM.

Example 

LCM (8, 14) = 56
HCF (8, 14) = 2

LCM (8, 14) × HCF (8, 14) = 56 × 2 = 112
8 × 14 = 112

Hence LCM (8, 14) × HCF (8, 14) = 8 × 14

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