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155 LearnersLast updated on November 29th, 2024
LCM of 4 and 16
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.
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.
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;
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.
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
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
Common Mistakes and how to avoid them while finding the LCM of 4 and 16
LCM of 4 and 16, Examples
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 ?
Explanation
Problem 2
The LCM of a and b is 16 and their HCF is 4, what is the product of a and b?
Explanation
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.
Explanation
FAQ’s on LCM of 4 and 16
1.What is the LCM of 4,8 and 16?
2.What is the LCM of 3,4 and 16?
3.What is the HCF of 4 and 16?
4.What is the LCM of 7 and 16?
5.What is the LCM of 8 and 16?
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.
Fun Fact
: She loves to read number jokes and games.
