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Last updated on November 29th, 2024

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LCM of 4 and 16

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Foundation
Intermediate
Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 4 and 16. 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.

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What is the LCM of 4 and 16?

The LCM of 4 and 16 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. 
 

 

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How to find the LCM of 4 and 16?

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

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LCM of 4 and 16 using the Listing multiples method

The LCM of 4 and 16 can be found using the following steps:


Step1: Write down the multiples of each number:  


Multiples of 4 = 4,8,12,16,…


Multiples of 16 = 16,32,…


Step2: Ascertain the smallest multiple from the listed multiples Of the numbers 4 and 16, 16 is the least common multiple.
 

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LCM of 4 and 16 using the Prime Factorization

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 16= 2×2×2×2×2


Prime factorization of 4 = 2×2

 

Step2: Multiply the highest power of each factor ascertained to get the LCM: 


LCM (4,16) = 16

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LCM of 4 and 16 using the Division Method

The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 


 Step1:Write down the numbers in a row

 

Step2:A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.

 

Step3:Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.


   
Step4:The LCM of the numbers is the product of the prime numbers in the first column, i.e, 


LCM (4,16) = 16

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Common Mistakes and how to avoid them while finding the LCM of 4 and 16

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LCM of 4 and 16, Examples

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Problem 1

The gardener waters the vegetable section every 4 days and the fruit section every 16 days. If he waters both sections today, after how many days will he water both sections on the same day ?

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Explanation

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Problem 2

The LCM of a and b is 16 and their HCF is 4, what is the product of a and b?

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Explanation

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Problem 3

The LCM of a and b is 18 and the product of a and b is 54, find the HCF of a and b.

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Explanation

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FAQ’s on LCM of 4 and 16

1.What is the LCM of 4,8 and 16?

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2.What is the LCM of 3,4 and 16?

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3.What is the HCF of 4 and 16?

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4.What is the LCM of 7 and 16?

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5.What is the LCM of 8 and 16?

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Important glossaries for LCM of 4 and 16

  • 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.

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Fun Fact

: She loves to read number jokes and games.

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