HCF and LCM - Important Terms - Factors, Multiples and Co-prime Numbers

HCF and LCM - Important Terms - Factors, Multiples and Co-prime Numbers

HCF and LCM are one of the important topic asked under Quantitative Aptitude  in any competitive exams either it be SSC, CGL, IBPS, RRB, or any Railways, Banking, State or Central government exams.

You should understand the concept of HCF and LCM properly as it will be further used in solving problems of time and work, pipes and cisterns etc.

Let's start the session !

Factors : All numbers which exactly divides other number are called factors of the number.

For example : The factors of 15 are 1, 3, 5, 15 as they divides 15 exactly i.e. leaves remainder 0 ( zero ) on division.

Common Factors : A common factors of two or more numbers are numbers which exactly divides each of them.

For example : 1, 2, 3 and 6 are common factors of 6 and 12.

Multiples : A number is said to be the multiple of other numbers if it is exactly divisible by other numbers.

For example : 15 is a multiple of 1, 3, 5, 15 as 15 is exactly divisible by 1, 3, 5 and 15

Common Multiple : A common multiple of two or more numbers is a number which is exactly divisible by each of them.

For example : 15 is a common multiple of 1, 3, 5 and 15.

HCF ( Highest Common Factor ) : H.C.F of two or more numbers is the greatest number which divides each number exactly.

For example : HCF of 12, 24 and 36 is 12 as 12 is the greatest numbers which divides 12, 24 and 36 exactly.

HCF ( Highest Common Factor ) is also known as GCF ( Greatest Common Factor )

LCM ( Lowest Common Multiple ) : The least number exactly divisible by two or more numbers is called least common multiple.

For example : LCM of 12, 24 and 36 is 36 as 36 is the least number which is exactly divisible by 12, 24 and 36

Co-prime Numbers : Two integers are said to be co-prime if the HCF ( highest Common Factor ) of them is 1.

For example : HCF of 17 and 23 is 1 and hence 17 and 23 are co-prime numbers

Now let's solve some questions to understand the concept properly !

Question 1 : Write all the factors of 125

Answer : 125 is exactly divisible by 1, 5, 25 and 125, So factors of 125 is 1, 5, 25 and 125

Question 2 : Write a number which is common multiple of 1, 2, 5 and 7

Answer : 70 is exactly divisible by 1, 2, 5 and 7, So common multiple of 1, 2, 5 and 7 is 70

Question 3 : Write all common factors of 15 and 25

Answer : 1 and 5 are common factors of 15 and 25


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