LCM (Least Common Multiple) and HCF (Highest Common Factor, also known as GCD or Greatest Common Divisor) are both concepts in mathematics dealing with factors and multiples of numbers, but they serve different purposes:
LCM (Least Common Multiple):
Definition: The smallest positive number that is a multiple of two or more numbers.
Purpose: Used when we need to find the smallest number that is divisible by all the given numbers.
Always greater than or equal to the largest number in the set.
Useful in adding or subtracting fractions with different denominators.
HCF (Highest Common Factor):
Definition: The largest positive integer that divides each of the numbers without a remainder.
Purpose: Used to find the largest number that can divide all the given numbers evenly.
Always less than or equal to the smallest number in the set.
Useful in simplifying fractions and solving certain types of problems involving divisibility.
Key Differences:
LCM is always greater than or equal to the largest number in the set, while HCF is always less than or equal to the smallest number in the set.
LCM is about finding multiples, while HCF is about finding factors.
LCM is used for addition and subtraction of fractions, while HCF is used for simplifying fractions.
The process of finding LCM often involves multiplication, while finding HCF often involves division.
Example:
For numbers 12 and 18:
LCM(12,18) = 36 (the smallest number divisible by both 12 and 18)
HCF(12,18) = 6 (the largest number that divides both 12 and 18 without remainder)
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LCM (Least Common Multiple) and HCF (Highest Common Factor) are two mathematical concepts that are often confused with each other but they are actually opposite in nature.
HCF (Highest Common Factor) also known as (Greatest Common Divisor)
LCM (Least Common Multiple)
You can watch a tutorial on how to find the HCF and LCM of two or more numbers
youtu.be/DheTDtoRdic
youtu.be/GP3-sWfuYwc
The GCF is 5. The LCM is 70. The difference is 65.
LCM is 20 and the hcf is 10
You seem to have misunderstood the difference between HCF and LCM. Ask your teacher to go over it again.
HCF = 3... LCM = 18 !
HCF is 60 and the LCM is 360
The HCF is: 2The LCM is: 2,520
hcf = 42, lcm = 84.
HCF is 48 and LCM is 576
hcf is 1 and LCM is 35
The HCF is always a factor of the LCM of two numbers. The HCF is a factor of both the numbers which are factors of their LCM. Thus the HCF is also a factor of the LCM of the two numbers.
Since the product of two numbers is equal to the product of their GCF and LCM, the GCF of two numbers is equal to their product divided by their LCM and their LCM is equal to their product divided by their GCF.
hcf: 1 lcm: 112,038