__LCM and HCF – Basic Concepts, Examples, Methods, Shortcuts, Math Tricks (Quantitative Aptitude made Simpler)__

## Formulas and Quick Tricks for LCM and HCF

- LCM stands for Least Common Multiple. The least number which is exactly divisible by each one of the given numbers is called their LCM
- HCF stands for Highest Common Factor. The other names for HCF are Greatest Common Divisor (GCD) and Greatest Common Measure (GCM)
- The HCF of two or more numbers is the greatest number that divides each one of them exactly.
- Two numbers are said to be co-prime if their HCF is 1
- HCF of fractions = HCF of numerators/LCM of denominators
- LCM of fractions = GCD of numerators/HCF of denominators

## Questions and Solved Examples on LCM and HCF

**Q.1:** The HCF of two numbers is 8. Which of the following can never be their LCM?

A. 24

B. 48

C. 56

D. 60

**Answer: **D. 60

**Explanation: **Watch the LCM and HCF Video for full explanation
**Q.2:** If the LCM of two numbers is 750 and their product is 18750, find the HCF of the numbers.

A. 25

B. 30

C. 50

D. 125

**Answer: **A. 25

**Explanation: **Watch the LCM and HCF Video for full explanation
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**Q.3:** LCM of 1/3, 5/6, 5/4, 10/7 is:

A. 10/11

B. 11/10

C. 10/7

D. 10

**Answer: **D. 10

**Explanation: **Watch the LCM and HCF Video for full explanation
**Q.4:** HCF of 3/16, 5/12, 7/8 is:

A. 1/48

B. 2/47

C. 3/47

D. 5/48

**Answer: **A. 1/48

**Explanation: **Watch the LCM and HCF Video for full explanation
**Q.5:** The least square number which divides 8, 12 and 18 is?

A. 64

B. 100

C. 144

D. 196

**Answer: **C. 144

**Explanation: **LCM = 72

72 * 2 = 144

**Q.6:** The least number which when divided by 8, 12 and 16, leave in each remainder 3, is?

A. 51

B. 61

C. 69

D. 71

**Answer: **A. 51

**Explanation: **LCM = 48 + 3 = 51

**Q.7:** The least number which when diminished by 7 is divisible by 21, 28, 36 and 45 is?

A. 1261

B. 1265

C. 1267

D. 1269

**Answer: **C. 1267

**Explanation: **LCM = 1260

1260 + 7 = 1267

**Q.8:** A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was Rs. 1189. Finally he was paid only Rs. 1073. For how many days did he actually work?

A. 35

B. 37

C. 39

D. 40

**Answer: **B. 37

**Explanation: **HCF of 1189, 1073 = 29

1073/29 = 37

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**Q.9:** An officer was appointed on maximum daily wages on contract money of Rs. 4956. But on being absent for some days, he was paid only Rs. 3894. For how many days was he absent?

A. 2

B. 3

C. 4

D. 5

**Answer: **B. 3

**Explanation: **HCF of 4956, 3894 = 354

(4956 – 3894)/354 = 3

**Q.10:** A merchant has three different types of milk: 435 liters, 493 liters and 551 liters. Find the least number of casks of equal size required to store all the milk without mixing.

A. 45

B. 47

C. 51

D. 61

**Answer: **C. 51

**Explanation: **HCF of 435, 493, 551 = 29

(453/29) + (493/29) + (551/29) = 51