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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 $=\dfrac{\text{LCM of Numerators}}{\text{HCF of Denominators}}$


Example 1: Find out LCM of $\dfrac{1}{2}$, $\dfrac{3}{8}$, $\dfrac{3}{4}$

LCM $=\dfrac{\text{LCM (1, 3, 3)}}{\text{HCF (2, 8, 4)}} = \dfrac{3}{2}$

Example 2: Find out LCM of $\dfrac{2}{5}$, $\dfrac{3}{10}$

LCM = $\dfrac{\text{LCM (2, 3)}}{\text{HCF (5, 10)}} = \dfrac{6}{5}$

Highest Common Multiple (HCF) of fractions

HCF of fractions $=\dfrac{\text{HCF of Numerators}}{\text{LCM of Denominators}}$


Example 1: Find out HCF of $\dfrac{3}{5}$, $\dfrac{6}{11}$, $\dfrac{9}{20}$

HCF $=\dfrac{\text{HCF (3, 6, 9)}}{\text{LCM (5, 11, 20)}} = \dfrac{3}{220}$

Example 2: Find out HCF of $\dfrac{4}{5}$, $\dfrac{2}{3}$

HCF = $\dfrac{\text{HCF (4, 2)}}{\text{LCM (5, 3)}} = \dfrac{2}{15}$

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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