- The sum of two numbers is 444 and their HCF is 37. Find all the possible pairs of such numbers?
- The LCM of two numbers is 12 times their HCF. The sum of LCM and HCF is 403 and if both the number are smaller than their LCM. Find both the numbers?
- The LCM of two numbers is 15 times their HCF. The sum of HCF and LCM of these numbers is 352.If one of the numbers is 110, find the other number.
- The HCF of each pair of 5 numbers is 3 and their LCM is 159. Find the multiplication of all the number.
- Three plots having an area of 210, 245 and 315 square meters respectively are to be sub-divided into equalised square flower beds. If the breadth of a bed ...
- The HCF of a^6 - 1 and a^4+ 2a^3- 2a-1 is
- The fruit-seller wants to pack the boxes with apples. If he packs 4 or 5 apples per box then he is left with 3 apples but if he packs with 8 or 9 apples ag...
- The HCF and LCM of two consecutive even number is 2 and 112 respectively. Find the sum of reciprocal of these two numbers?
- The ratio of two number is 13 : 10 and their HCF is 25. then find out their LCM?
- The LCM of two numbers is 12 times their HCF. The sum of LCM and HCF is 403 and if both the number are smaller than their LCM. Find both the numbers?
- Find the total number of Prime factor in the given expression? 315 × 56 × 68
- Find the smallest number which when divided by 3, 4, 5 and 6 gives remainder ‘2’ in each case?
- Sum of the two numbers is 42. LCM and HCF of that two number is 72 and 6 respectively. Find the sum of reciprocals of the numbers?
- Find the least number of equal sizes square tiles which can be fitted in a rectangular room whose sides are 360 m and 480 m?
- LCM of two numbers is 64 times of their HCF. Sum of the HCF and LCM is 975. If the first number is 960. Find the other number?
- Sum of the two numbers is 80. LCM and HCF of that two number is 168 and 8 respectively. Find the difference of the numbers?
- The least multiple of 19, which on dividing by 5,6,7,8 and 9 leaves remainder 2 in each case is
- Find the largest number of the five digit which is exactly divisible by 48, 72 and 108. ...
- The ratio of two number is 6 : 5 and their HCF is 15. So find and their LCM?
- Two men started moving in a circular path from the same place at the same time in the same direction. If they complete one revolution in 12 min and 16 min ...
- If the ratio of two numbers is 8 : 9 and their HCF is 6 then their LCM will be : ...
- If HCF of two numbers is 16 then which of the following can never be their LCM? ...
- If HCF of two numbers is 11 then which of the following can never be their LCM?
- If HCF of two numbers is 27 then which of the following can never be their LCM? ...
- Find the greatest number which when divide 33,55 & 77 leave a same remainder in each case? ...
- Find the greatest number which when divide 25,40 & 55 leave a same remainder in each case? ...
- Five bells commence tolling together and tolls at intervals of 2, 6, 10, 18 and 24 seconds respectively. In 36 minutes, how many times do they toll togethe...
- Five bells commence tolling together and tolls at intervals of 6, 12, 36, 42 and 60 seconds respectively. In 126 minutes, how many times do they toll toget...
- The least number which is exactly divisible by 10,15 and 20 is ...
- The least number which is exactly divisible by 9, 27 and 36 is ...
- The least number which when divided by 8,16,22 and 32 leave a same remainder 1 in each case? ...
- The least number which when divided by 12, 27 and 39 leave remainder 8, 23 and 35 respectively is? ...
- The H.C.F of two numbers is 2 and their L.C.M is 117. If one of the numbers is 13, find the other?
- The H.C.F of two numbers is 8 and their L.C.M is 136. If one of the numbers is 64, find the other?
- The sum of two numbers is 65 and their HCF is 13. Total number of such pairs of numbers is?
- The sum of two numbers is 126 and their HCF is 14. Total number of such pairs of numbers is?
- The sum of two numbers is 99 and their HCF is 11. Total number of such pairs of numbers is?
- The sum of two numbers is 104 and their HCF is 13. Total number of such pairs of numbers is? ...
- The sum of two numbers is 96 and their HCF is 24. Total number of such pairs of numbers is? ...
- The product of two numbers is 10140 and their HCF is 13. Total number of such pairs of numbers is? ...

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The Highest Common Factor (HCF) and the Least Common Multiple (LCM) are a part of the Quantitative Aptitude syllabus for government competitive examinations for SBI PO, SBI Clerk, IBPS PO, IBPS Clerk, LIC AAO, SSC CGL, SSC CHSL and railways. The HCF is the greatest factor present between the given two or more numbers. It is the highest number that can be divided into 2 or more numbers without leaving any remainders. Whereas, LCM is the smallest factor by which two or more given numbers may exactly be divided. HCF is also referred to as the greatest common factor and LCM is also known as the least common divisor.

There are mainly 3 methods to derive the HCF and LCM of a given set of numbers. They are;

- Factorization method:

HCF: Firstly, the multiple factors of all the given numbers are listed. Then, the highest factor which is common to all the numbers is the HCF.

E.g., find the HCF of 36 and 45.

36: 1, 2, 3, 4, 6, 9, 12, 18, 36

45: 1, 3, 5, 9, 45

While 1, 3 and 9 are all common to 36 and 45, the number of greatest value common to both is 9.

HCF= 9.

LCM:

Find the LCM Of 25 and 30

25= 25, 50, 75, 100, 125, 150, 175, 200

30= 30, 60, 90, 120, 150, 180, 210

The lowest factor common to both is 150.

∴ LCM= 150

- Long Division method: In a given set of numbers, consider the smallest number to the divisor and the larger number(s) as the dividend. Keep dividing using the long division method until the remainder achieved is 0.

HCF: Find the HCF of 24 and 48

1

24⟌36

2

6 ⟌12

-12

0

∴ HCF= 6

LCM:

Find the LCM of 24 and 36.

2⟌24, 36

2⟌12, 18

2⟌6, 9

2⟌3,9

3⟌1,3

3⟌1,1

LCM= 2x2x2x2x3x3= 144

∴LCM=144

- Prime Factorization method: List all the factors via which the provided numbers can be accurately divided to express all the numbers as a product of their prime numbers. The largest factor common to all the numbers is the HCF.

HCF: The Prime factor

E.g., find the HCF of 30, 36 and 42.

30=2x3x5

36=2x2x3x3x3

45= 2x3x7

3 is the greatest number that divides all the given numbers. Thus 3 is the HCF of 30, 36 and 45.

LCM:

Find the LCM of 25 and 30

25= 5x5

30= 2x3x5

LCM= 5X2X3X5= 150

∴ LCM= 150

Relationship between HCF and LCM.

- The product of the HCF and LCM of any two given numbers is always equal to the product of the two given numbers. However, this rule applies to a pair of two numbers only and not more. Formula: product of 2 numbers = (HCF of the two numbers) x (LCM of the two numbers)
- Since the HCF of co-prime numbers is 1, the LCM of the given co-prime numbers is equal to the product of the numbers.

Formula: LCM of co-prime numbers= product of the co-prime numbers.

Of fractions;

HCF of fractions= HCF of numerator / LCM of denominator

LCM of fractions= LCM of Numerator / HCF of Denominator

While HCF and LCM questions are always assessed in multiple-choice question (MCQ) format, the pattern of questions asked may not always be the same. Rather than simply providing numbers and asking for their HCFs and LCMs, sometimes, the HCF and/or LCM may be provided with one or more numbers and the question might ask to find the other number from the set.

E.g., The HCF of two numbers is 4 and the LCM of the same is 6528. If one number is 204, find the other number.

- 240
- 128
- 328
- 186

We will use the prime factorization method to solve this question.

204= 2x2x3x17

The prime factors of the provided options are only 240

240= 2 × 2 × 2 × 2 × 3 × 5

128= 2x2x2x2x2x2x2

328= 2x2x2x41

186= 2x2x2x23

Thus, we can see that from the given options, only the 128 can have an HCF of 4 with 204. Therefore, the correct answer is option b.

Applications of HCF and LCM.

HCF:

- Two divide something into groups and rows/columns.
- To split something into smaller portions.
- To equally distribute something into the largest group possible.

LCM:

- To buy/ purchase multiple items to have enough to be divided among a certain number.
- To analyze the repetitive pattern of events.

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