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Last updated on November 29th, 2024

LCM of 3 and 4

Q: Why is the LCM of 3 and 4 not simply their product (4 × 3 = 12) ?

No, multiplying gives you the product of the numbers, in this case,12. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.

Q: What is the GCF (Greatest common factor) of 3 and 4?

List down the prime factors of the numbers Prime factors of 3 = 3 Prime factors of 4 = 22 Find the common prime factors —> 3,2,2 Pick the lowest power of the common factor —> None HCF of 3,4= 1, since there are no common factors between the given numbers.

Q: What is the LCM of √3 and √4 ?

Follow the below steps to find the LCM of √3 and √4; Factorize; √3 is already in its simplest form. √4 —> 2 Find the highest powers of the prime factors; √3 — the prime factor —> 3, exponent of 0.5 (√3 = 30.5) 2 — the prime factor —> 2 with an exponent of 1 (2 = 21) Combine the ascertained highest powers; LCM of √3 and √4 = 21 × 30.5 The above simplifies to —> 2 x √3 LCM = 2√3

Q: What is the LCM of 3,4 and 7?

Follow the below steps to find the LCM of 3,4 and 7; Find the prime factors of the numbers: Prime factorization of 3 = 3 Prime factorization of 4 = 2 × 2 Prime factorization of 7 = 7 × 1 Take the highest powers of each prime factor: Multiply the highest powers to get the LCM: LCM(3, 4,7)= 84

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 4. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 3 and 4?

The LCM of 3 and 4 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.

How to Find the LCM of 3 and 4?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

LCM of 3 and 4 using the Listing Multiples Method

The LCM of 3 and 4 can be found using the following steps:

Step 1:Write down the multiples of each number

Multiples of 3 = 3, 6, 9,12 …

Multiples of 4 = 4, 8,12 …

Step 2: Ascertain the smallest multiple from the listed multiples

The least common multiple is 12.

LCM of 3 and 4 using the Prime Factorization Method

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Step1: Find the prime factors of the numbers:

Prime factorization of 3 = 3

Prime factorization of 4 = 2 × 2

Step2:Take the highest powers of each prime factor:

Multiply the highest powers to get the LCM

LCM(3, 4) = 12

LCM of 3 and 4 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.

Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

Step 2: continue the division till we reach to 1.

3 ×2 ×2 =12

Thus, LCM(3, 4) = 12

Common Mistakes and how to avoid them in LCM of 3 and 4

LCM of 3 and 4, Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Solve; 3/1+4/1

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

Problem 2

Goods are received by a shipping company every 3 and 4 days. If the shipments have been received today, when will they next arrive on the same day?

Explanation

Problem 3

a= 3, b=4, verify the relationship → a×b/LCM(a,b)=HCF(a,b) holds.

Explanation

FAQs on LCM of 3 and 4

1. Why is the LCM of 3 and 4 not simply their product (4 × 3 = 12) ?

2. What is the GCF (Greatest common factor) of 3 and 4?

3.What is the LCM of √3 and √4 ?

4. What is the LCM of 3,4 and 7?

5.What are the multiples of 3 and 4?

Important glossaries for the LCM of 3 and 4

Multiple: A number and any integer multiplied.

Prime Factor: A natural number (other than 1) that has factors that are one and itself.

Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.

Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.

Relatively Prime Numbers:Numbers that have no common factors other than 1.

Fraction: A representation of a part of a whole.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.