If you are preparing for competitive examinations (conducted by state PSC, SSC, and UPSC), one of the repeated sections in quantitative aptitude is the LCM and HCF.
You can expect questions that require skills in LCM and HCF calculations. If you prepare, you can score 100 percent on this part.
L.C.M
L.C.M. (Least Common Multiple) is the least non-zero number in common multiples of two or more numbers.
H.C.F
H.C.F. (Highest Common Factor) is the highest common factor of two or more numbers.
This tutorial teaches students to solve arithmetic questions based on L.C.M and H.C.F in the bank and PSC question papers.
Let us check some facts and formulas to help you solve questions in competitive exams by Banks, State and Central Governments' Job Recruiting agencies, etc.
Division Method to Find LCM and HCF
Before going for methods to solve LCM and HCF questions asked in aptitude examinations, let us check the methods to find these values using the division method.
1) Find the LCM of 12, 17, and 30 using the division method
| 2 | 12, 17, 30 --------------------- |6, 17, 15 2 | -------------------------------- 3 |3, 17, 5 | ----------------------- 1, 17, 5 LCM = 2 X 2 X 3 X 17 X 5 = 1020
2 ) Find the HCF of 24, 40, and 64 using the division method
| 2 | 24, 40, 64 --------------------- |12, 20, 32 2 | -------------------------------- 2 |6, 10, 16 | ----------------------- 3, 5, 8
HCF = 2 X 2 X 2 = 8
Important Formulas to Solve Competitive Examination Questions
- The Product of two numbers = Product of LCM and HCF of those numbers
ie:P x Q = L x H where L is LCM and H is HCF of two numbers P and Q.
- LCM = (P x Q) / HCF
- HCF = (P x Q) / LCM
- P = (LCM x HCF ) / Q
- Find the LCM of fractions
To find the LCM of fractions, divide the LCM of numerators by the HCF of denominators
- Find the H.C.F. of fractions
To find the H.C.F. of fractions, divide the H.C.F. of numerators by L.C.M. of denominators
Solved examples
1) H.C.F. of two numbers is 2 and L.C.M. is 180. One of the two numbers is 10. Find the second number.
According to our formula, P = (LCM x HCF ) / Q so P = (2 x 180 ) / 10 =36
The second number is 36.
Hints
If you are asked to find the least number divisible by a set of numbers, all you have to find is the L.C.M.
L.C.M. of a given set of numbers must be either the biggest number or bigger than the biggest number in the list
H.F.C. of a given set of numbers would be either the smallest or lower than the smallest number.
GJR Institute (G_{overnment}J_{obs}R_{ecruitment}.^{in}) offers special coaching to SSC and PSC students to crack arithmetic questions. We conduct SSC and PSC classes seven days a week.
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