In order to learn about HCF (highest common factor) and LCM (least common multiple), one should know about two important concepts: factors and multiples. Without the prior knowledge of factors and multiples, one cannot understand LCM and HCF questions (by HCF division method).
What are factors and why they are important for LCM and HCF questions?
Factor is such a number which when comes in the table of a specific number, then all those numbers will be called as that number’s factor.
For instance, if we have a number 15, so 15 comes in the tables of which numbers? Clearly, 15 comes in the table of 1 (1 x 15=15), 3 (3 x 5=15), 5 (5x 3=15), and 15 itself (15×1=15). Thus, the factors of 15 are 1, 3, and 5. (We will not write 15 because it has already been represented by 1).
Always remember that 1 is the factor of all numbers.
How to find factors of a number through HCF division method?
How to find factors of a number?
The easiest way to find the factors of a number is by the divisional method. This method can be understand with help of an example.
Example: Find factors of 15. 5 15 3 3 1 Factors of 15 = 1 x 3 x 5
What are multiples and why they are important for LCM and HCF questions?
All numbers that comes in the table of a number are its multiples. For example, multiple of 15 are 15, 30, 45…, and so on.
How to find multiples of a number?
In order to find multiples of a number, just use the multiplication tables.
| Factors of 15 | Multiples of 15 |
| 1 x 15 = 15 x 1 = 15 ==> 1 | 15 x 1 = 15 |
| 3 x 5 = 15 ==> 3 | 15 x 2 = 30 |
| 5 x 3 = 15 ==> 5 | 15 x 3 = 45 |
| – | … |
What is HCF and how to calculate HCF of a number (HCF division method)?
What is HCF and how to calculate HCF of a number?
HCF is the largest of all the common factors. It is also called GCD (Greatest Common Divisor or Greatest Common Denominator). HCF can be calculated with help of a formula which is:
HCF = product of common factors
The best way to understand HCF calculation is by example.
Find the HCF of 24 and 36. Solution: 2 24 2 36 2 12 2 18 2 6 3 9 3 3 3 3 1 1 Factors of 24 = 1 2 2 2 3 Factors of 36 = 1 2 2 3 3 Common Factors = 1 x 2 x 2 x 3 = 12 HCF = Product of common factors = 12
What is LCM and how to calculate LCM of a number through HCF division method?
What is LCM and how to calculate LCM of a number?
LCM is the smallest number that is a multiple of two or more numbers. It is the abbreviation of least common multiple. LCM can be calculated with the help of a formula which is:
LCM = common factors x uncommon factors
or
LCM = HCF x All other factors (in special cases)
The best way to understand LCM calculation is with the help of an example.
Find the LCM of 144 and 232. Solution: 2 144 2 232 2 72 2 116 2 36 2 58 2 18 29 29 3 9 1 3 3 1 Factors of 144 = 1 2 2 2 2 3 3 Factors of 232 = 1 2 2 2 29 Common Factors = 1x2x2x2 = 8 Uncommon Factors= 2x3x3x29 = 522 LCM = Product of common x uncommon factors = 8 x 522 = 4176
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