What Is the LCM of 26 and 91

The concept of LCM of 26 and 91 is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Finding the least common multiple of two numbers is especially useful in dealing with fractions, scheduling, and class 10 board exam questions.

Understanding LCM of 26 and 91

The LCM of 26 and 91 (Least Common Multiple) is the smallest number that is exactly divisible by both 26 and 91. This concept is widely used in fraction addition/subtraction, solving time-based problems in maths, and exam revision sessions. Knowing how to find the LCM using prime factorization and the division method is an important skill for students preparing for school and competitive exams.

Formula Used in LCM of 26 and 91

The standard formula is: \( \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \)

For manual calculation, the LCM can be found by taking all the prime factors from both numbers, using the highest powers present.

Finding the LCM of 26 and 91 - Stepwise Methods

Method 1: Prime Factorization

1. Find prime factors of both numbers.

2. List all unique prime factors (use each common factor only once, with its highest power).


3. Multiply these prime factors:


Therefore, LCM(26, 91) = 182.

Method 2: Division (Ladder) Method

1. Write numbers 26 and 91 side by side.

2. Divide both numbers by the smallest prime number that divides at least one of them. For each step, bring the quotient below.

3. Multiply all the divisors used: 2 × 7 × 13 = 182

So, LCM(26, 91) = 182.

LCM and HCF Relationship for 26 and 91

The relationship between LCM and HCF (Highest Common Factor) is vital in exams. The formula is:

LCM × HCF = Product of the numbers

For 26 and 91: HCF = 13 (since 13 is the highest number that divides both).
Check: 182 × 13 = 2366
Also, 26 × 91 = 2366. The relation holds true!

Here’s a helpful table to understand the LCM of 26 and 91 more clearly:

LCM and HCF Table for 26 and 91

Number	Prime Factors	HCF	LCM
26	2 × 13	13	182
91	7 × 13

This table shows the factor breakdown and makes it easy to check the answer during exams.

Worked Example – Solving LCM of 26 and 91

1. Write both numbers: 26 and 91.

2. Find prime factors:

3. LCM must include each prime factor at the highest power:

4. Multiply all the selected prime factors:

Practice Problems

• Find the LCM of 26 and another number, like 39 or 65.
• If HCF(26, x) = 13 and LCM(26, x) = 182, what is x?
• List the common multiples of 26 and 91 up to 500.
• What is the LCM of 26, 91, and 13?

Common Mistakes to Avoid

• Confusing LCM with HCF – remember LCM is the smallest number divisible by both, HCF is the largest that divides both.
• Omitting common primes or repeating shared factors in multiplication (use each common factor only once with the highest power).
• Not checking the answer using the product-HCF-LCM relationship.

Real-World Applications

The concept of LCM of 26 and 91 appears in areas such as adding/subtracting unlike fractions, synchronizing events (e.g., two lights blinking every 26 and 91 seconds), and timetable management. Vedantu helps students see how these maths skills apply both in exams and in real life.

We explored the idea of LCM of 26 and 91, how to apply it with step-by-step solutions, check the result with the HCF-LCM relationship, and reviewed real-life uses. Practice more with Vedantu to build strong foundations in such topics and gain confidence for your board exams.

Related Learning Resources

• Prime Numbers: Useful for understanding how to break down numbers for LCM.
• LCM and HCF: Deep dive into their relationship, formulas, and differences.
• Factors of 91: Discover factorization details for better LCM calculation.
• Fundamental Theorem of Arithmetic: Learn why unique prime factorization matters for LCM.
• Multiples: Understand the idea of common multiples for LCM problems.
• LCM by Prime Factorization Method: View more solved examples stepwise.
• HCF by Long Division Method: Useful for co-practicing HCF and verifying LCM answers.
• Properties of HCF and LCM: For proofs and deeper mathematical understanding.
• Tables 2 to 20: Quick reference for multiplication during exam time.
• Factors of a Number: Foundation for any type of factor-based problem.