Quant Booster Dose – HCF and LCM Questions PDF
HCF and LCM Question PDF with Answers for government exams like SSC, Railways, Banking, FCI, CWC, Insurance Exams, UPSC, and other state PCS exams. As we all know in many competitive exams in Quantitative Aptitude/ Numerical Ability subject HCF and LCM Questions asked repeatedly, so you cannot ignore the HCF and LCM Questions PDF.
As questions are based on previous year papers, there are chances that candidates will find many questions from the HCF and LCM Questions with Answers PDF in all competitive Exams. If you check the last 4-5 year’s papers of SSC, Railways and Banking Exams, you will find that many different types of Algebra questions are asked. Today we have compiled “150+ HCF and LCM Questions PDF with Answers for SSC, Railway & Banking Exam”. You can download Free HCF and LCM Questions with Solution so that you get all the important questions at one place. And it will become very easy for you guys to revise them.
HCF and LCM Questions PDF for SSC, Railways and Banking Exams
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HCF and LCM Questions with Answers | Download Free PDF
What is HCF and LCM?
HCF (Highest Common Factor) and LCM (Least Common Multiple) are fundamental concepts in mathematics, particularly in number theory. HCF is the highest common number which can exactly divide the two given numbers. LCM or Lowest Common Multiple is the common number that is divisible by both the given numbers. These concepts are essential tools for solving a wide range of mathematical problems. There are different formulas and methods for finding HCF and LCM of two or more numbers, such as the division or prime factorization methods.
- HCF Definition: The Highest Common Factor (HCF) of 2 or more numbers is defined as the greatest possible number that divides both the numbers completely. For example, if “a” and “b” are the two numbers, then the HCF of a and b, i.e, HCF (a, b) is the greatest possible number that divides both a and b.
- LCM Definition: The Least Common Multiple (LCM) of 2 or more given numbers is defined as the smallest common multiple, which is found in both the numbers. The LCM of any given number can also be found using the listing multiples method and prime factorisation method.
How to solve HCF and LCM Questions
There are two main ways to find HCF and LCM-
- Prime Factorization method
- Division method
HCF of two numbers by Prime Factorization
We find the prime factors of the supplied numbers to find the HCF of those numbers using prime factorization. We find the product of the prime factors that are common to each of the given numbers after we’ve found the factors. Let’s use the prime factorization method to find the HCF of 50 and 75, for example.
50 = 2 x 5 x 5 are the prime factors.
75 = 3 x 5 x 5 are the prime factors.
The common factor between 50 and 75 is 5 x 5. As a result, the HCF of (50, 75) = 25.
LCM of two numbers using Prime Factorization
Following the procedures below, we can calculate the LCM of any two numbers using the prime factorization method:
Step 1: Make a list of the prime factors of the provided numbers, noting which ones are common.
Step 2: The LCM of the given numbers is equal to the product of the numbers’ common prime factors and unusual prime factors.
Note that common components will only be mentioned once.
Let’s use prime factorization to find the LCM of 160 and 90.
Step 1: The prime factors of 160 = 2 x 2 x 2 x 2 x 2 x 2 x 5 and 90 = 2 x 3 x 3 x 3 x 5 are added together.
Step 2: Add all the prime factors together = Common prime factors (2 x 5) Uncommon prime factors (2 x 2 x 2 x 2 x 3 x 3) = 1440.
As a result, the LCM of 160 and 90 is 1440.
HCF of two numbers using Division Method
HCF and LCM can be calculated in two ways using the division method.
Follow the steps below to find the HCF using the division method:
Step 1: To begin, divide the larger number by the smaller number and examine the remainder.
Step 2: Perform the division again, using the residual of the previous step as the divisor and the divisor of the previous step as the dividend.
Step 3: Continue dividing until the remainder is not equal to zero.
Step 4: The HCF of the given numbers will be the final divisor.
For example, to find the HCF of 144 and 160.
Since 160>144, so the dividend will be 160 and the divisor will be 144.
By using the division method, we get:
As a result, the largest number that divides 160 and 144 is 16.
As a result, HCF (144, 160) = 16.
LCM of two numbers using Division Method
We divide the numbers using prime numbers and terminate the division process when we receive only 1 in the final row to find the LCM of numbers using the division method.
Step 1: Multiply the numbers by the smallest prime number, ensuring that the prime number divides at least one of the given numbers.
Step 2: Write the quotients just beneath the next row’s numbers.
Step 3: Assume the above quotients are the new dividends for the following division step.
Step 4: Consider another prime number that divides at least one of the dividends perfectly.
Step 5: Repeat Steps 1–5 until we have 1 in the last row
For example, to find the LCM of 60 and 45
2 | 60, 45
2 | 30, 45
2 | 15, 45
2 | 5, 15
2 | 5, 5
5 | 1, 1
Hence, LCM of 60 and 45 is 2 × 2 x 3 × 3 × 5 = 180
Tips and Tricks and Shortcuts for solving HCF & LCM Questions
- The H.C.F of two or more numbers is smaller than or equal to the smallest number of given numbers
- The smallest number which is exactly divisible by a, b and c is L.C.M of a, b, c.
- The L.C.M of two or more numbers is greater than or equal to the greatest number of given numbers.
- The smallest number which when divided by a, b and c leaves a remainder R in each case. Required number = (L.C.M of a, b, c) + R
- The greatest number which divides a, b and c to leave the remainder R is H.C.F of (a – R), (b – R) and (c – R)
- The greatest number which divide x, y, z to leave remainders a, b, c is H.C.F of (x – a), (y – b) and (z – c)
- The smallest number which when divided by x, y and z leaves remainder of a, b, c (x – a), (y – b), (z – c) are multiples of M
Required number = (L.C.M of x, y and z) – M
Why Quantitative Aptitude HCF and LCM Questions PDF is Important for Exams?
- All the questions prepare by Exams experts.
- The practice questions covered are across the levels i.e. Easy, Moderate, and Difficult.
- Provides a detailed approach to the solution of each question.
- Focuses on all the new patterns and advanced-level type questions.
- HCF and LCM Questions PDF boosts confidence and reduces pre-exam jitters by regularly attempting a variety of questions and tackling the difficulty level expected in the final exam.
This Quant Booster Dose HCF and LCM Questions PDF is useful for the upcoming Banking and Insurance exams i.e. IBPS PO, SBI PO, Clerk, IBPS RRB PO & Clerk, RBI Assistant, RBI Grade B, NABARD, LIC AAO, SSC (CGL, CHSL, MTS, CPO, and Constable), Railway RRB (NTPC, Group D, JE, ALP) & Other Government Exams.
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