LCM of 336 and 54

LCM of 336 and 54 is 3024. LCM of any two is the value that is divisible by the two given numbers. LCM stands for Least Common Multiple. It is also called Least Common Divisor (LCD). In the Least Common Multiple, a common multiple is nothing but a number which is a multiple of two or more numbers.

In this article, we will learn about LCM of 336 and 54, Definition of LCM, and How to Find LCM of 336 and 54 using various methods like Prime Factorization, Listing Multiples, Long Division Method, and others.

What is LCM of 336 and 54?

LCM of two positive integers, 336 and 54, is the smallest positive integer which is divisible by both 336 and 54 with no remainder. In this case, the smallest possible divisor is 3024.

LCM of 336 and 54 is 3024

LCM Definition

LCM (Least Common Multiple) is the smallest common multiple between any two or more numbers. LCM of two numbers follows Associative Property, Distributive Property, and Commutative Property.

Let us understand LCM by taking two numbers, 2 and 7, and find their LCM

• Factors of 2 are 2, 4, 6, 8, 10, 12, 14, 16 and so on.
• Factors of 7 are 7, 14, 21, 28, and so on.

LCM of two numbers is the value that is evenly divisible by the given two numbers. We can see from the above example that the first common multiple which is divisible by both 2 and 7 is 14. Therefore, according to the definition of LCM, the least common multiple of 2 and 7 is 14.

LCM of 336 and 54 Calculator

How to Find LCM of 336 and 54

LCM of any two numbers is generally found using 3 ways. We will discuss all three ways in detail below,

• LCM of 336 and 54 by Prime Factorization
• LCM of 336 and 54 by Listing Multiples
• LCM of 336 and 54 by Long Division

LCM of 336 and 54 by Prime Factorization

Main steps for finding LCM of 336 and 54 by prime factorization method:

• Apply repeated division method to find the prime factors of the given numbers.
• Represent the numbers in their exponent form and after representing it, find the product of only those prime factors that have the highest power.
• The product of these factors with the highest powers is the LCM of the given numbers.

Prime factorization of 336 and 54, respectively, is given by:

336 = 2 × 2 × 2 × 2 × 3 × 7 = 2⁴ × 3 × 7

54 = 2 × 3 × 3 × 3 = 2 × 3³

LCM = 2⁴ × 3³ × 7

LCM (336, 54) = 3024

LCM of 336 and 54 by Listing Multiples

Steps for finding LCM of 336 and 54 by listing multiples:

• List first few multiples of both A and B.
• Mark the common multiples from multiples of both numbers.
• Select the smallest common multiple. That lowest common multiple is the LCM of two numbers.

To calculate the LCM of 336 and 54 by listing out the common multiples, list the multiples as:

Multiples of 336 = 336, 672, 1008, 1344, 1680, 2016, 2352, 2688, 3024, 3360

Multiples of 54 = 54, 108, 162, 216, 270, 324, 378,…., 3024

Here, 3024 is first common multiple of both 336 and 54.

Therefore, LCM (336, 54) = 3024

LCM of 336 and 54 by Long Division

Below are steps for finding LCM of 336 and 54 by long division method:

• Divide the numbers, by smallest prime number and if any number is not divisible, then write down that number and proceed further.
• Keep on dividing the row of numbers by prime numbers, unless we get the result as 1 in the complete row.
• Now, LCM of the numbers will be equal to the product of all the prime numbers we obtained in the division method.

To calculate LCM of 336 and 54 by division method, we will divide numbers by their prime factors as shown:

336 = 2 × 2 × 2 × 2 × 3 × 7

54 = 2 × 3 × 3 × 3

LCM (336, 54) = 3024

LCM vs HCF of 336 and 54

Highest Common Factor of 336 and 54 is 6 and the Least Common Multiple of 336 and 54 is 3024.

LCM × HCF = Product of Two Numbers

336 = 2 × 2 × 2 × 2 × 3 × 7

54 = 2 × 3 × 3 × 3

LCM (336, 54) = 3024

HCF (336, 54) = 6

Example on LCM of 336 and 54

Some solved examples on lCM of 336 and 54 are,

Example 1: Find HCF and LCM of 336 and 54 by Prime Factorization.

Solution:

Factors of 336 and 54,

336 = 2 × 2 × 2 × 2 × 3 × 7

54 = 2 × 3 × 3 × 3

LCM (336, 54) = 2 × 2 × 2 × 2× 3 × 3 × 3× 7

LCM (336, 54) = 3024

Example 2: Verify Relationship between GCF and LCM of 336 and 54.

Solution:

336 = 2 × 2 × 2 × 2 × 3 × 7

54 = 2 × 3 × 3 × 3

LCM (336, 54) = 3024

GCF (336, 54) = 6

LCM(336, 54) × GCF(336, 54) = Product of 336, 54

3024 × 6 = 336 × 54

18144 = 18144 (Verified)

Example 3: For two numbers, HCF = 6 and LCM = 3024. If one number is 54, find the other number.

Solution:

Assume other number to be x

GCD × LCM = 54 × x

x = (GCD × LCM)/54

x = (6 × 3024)/54

x = 336

Therefore, other number is 336.

Practice Problems on LCM of 336 and 54

Various problems on on LCM of 336 and 54 are,

P1. Find LCM of 88 and 104 by prime factorization method.

P2. Find LCM if the product of two numbers is 1026 and the GCD is 54.

P3. GCD and LCM of two numbers are 6 and 946 respectively. If one number is 244, find the other number.

P4. Find LCM of 9 and 11 by listing multiples.

FAQs on LCM of 336 and 54

What is LCM of 336 and 54?

LCM of 336 and 54 is 3024.

What is LCM and HCF of 336 and 54?

Highest Common Factor of 336 and 54 is 6 and Least Common Multiple of 336 and 54 is 3024.

What is Relation between HCF and LCM?

LCM × HCF = Product of Two Numbers

What are Methods Used to Find LCM of 336 and 54.

Methods used to find LCM of 336 and 54 are:

• Prime Factorization Method
• Division Method
• Listing Multiples