Relation between HCF and LCM

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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
Least Common Multiple (LCM) of fractions
LCM of fractions =LCM of NumeratorsHCF of Denominators


Example 1: Find out LCM of 12, 38, 34
LCM =LCM (1, 3, 3)HCF (2, 8, 4)=32
Example 2: Find out LCM of 25, 310
LCM = LCM (2, 3)HCF (5, 10)=65
Highest Common Multiple (HCF) of fractions
HCF of fractions =HCF of NumeratorsLCM of Denominators


Example 1: Find out HCF of 35, 611, 920
HCF =HCF (3, 6, 9)LCM (5, 11, 20)=3220
Example 2: Find out HCF of 45, 23
HCF = HCF (4, 2)LCM (5, 3)=215
How to calculate LCM and HCF of DecimalsStep 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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