340 LearnersLast updated on May 26th, 2025
LCM of 15,20 and 25
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 15,20 and 25. 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 15,20 and 25?
The LCM of 15,20 and 25 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 15,20 and 25?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 15,20 and 25 using the Listing Multiples Method
The LCM of 15,20 and 25 can be found using the following steps:
Step1: Write down the multiples of each number
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,165,180…300
Multiples of 20= 20,40,60,80,100,120,140,160,180,…300
Multiples of 25 = 25,50,75,100,125,150,175,200…300
Step2: Ascertain the smallest multiple from the listed multiples
The smallest common multiple is 300
Thus, LCM (15,20,25) = 300
LCM of 15,20 and 25 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.
Step 1: Find the prime factors of the numbers:
Prime factorization of 15 = 5×3
Prime factorization of 20 = 5×2×2
Prime factorization of 25 = 5×5
Step2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:
5×3×2×2×5 = 300
LCM (15,20,25) = 300
LCM of 15,20 and 25 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: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.bring down the numbers not divisible by the previously chosen prime number.
Step 3:Continue dividing the numbers until the last row of the results is ‘1’ .
2×2×3×5×5 = 300
Thus, LCM (15,20,25) = 300
Common Mistakes and how to avoid them while finding the LCM of 15,20 and 25
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 15,20 and 25, make a note
while practising.
Mistake 1
Not recognizing shared multiples
One may list 60 as the multiple of both 20 and 15 but fail to check if it is a multiple of 25. To avoid the same, thoroughly check before proceeding.
LCM of 15,20 and 25, examples
Problem 1
LCM of 15 and x is 60. Find x.
LCM(15,x) = 60
LCM(a,b)=a×b/HCF(a,b)
Let x be;
LCM(15,x) = 15×x/HCF(15,x) = 60
Let’s analyze x as;
Prime factorization of 15 = 5×3
Prime factorization of 60 = 5×2×2×3
For the LCM to be 60, x should contribute 22 to the LCM;
x could be 20; 22×5 = 20
Let us now verify the above assumption;
HCF(15,20) = 5
LCM(15,20) = 15×20/5= 60
Explanation
After the above verification, we can say that the missing number is 20.
Problem 2
LCM (15,20,25) = x. Find the smallest positive integer (n), where n×x is a multiple of 60.
LCM (15,20,25) = x
We ascertained the LCM of 15,20,25 from the previous calculations.
LCM (15,20,25) = 300
n is;
n×300 is a multiple of 60
Te same can be rearranged as;
n×300 = k×60, for some integer k
Divide both the sides 60;
n×5 = k
n×5 = k implies that n is to be a multiple of 12, 300/60 = 5 and n to be a multiple of 1/5.
Smallest n = 12
Explanation
n is 12, as elaborated above. It satisfies the condition laid the smallest positive integer (n), where n×x is a multiple of 60.
Problem 3
a =15, b=20, c=25, use the formula for the LCM of three numbers.
The formula used to find the LCM of 3 digits is;
LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)
To apply the above formula, calculate the LCM of 15 and 20 first;
Prime factorization of 15 = 5×3
Prime factorization of 20 = 5×4
LCM (15,20) = 60
Next, find the HCF of 60 (LCM of 15 and 20) and 25;
Factors of 60 = 1,2,3,4,5,6,10,12,15,20,30,60
Factors of 25 = 1,5,25
HCF(60,25) = 5
We can now substitute the ascertained values into the formula;
LCM(a,b,c) = LCM(a,b)×c/HCF(LCM(a,b)c)
LCM(15,20,25) = LCM(15,20)×25/5
LCM(15,20,25) = 60×25/5 = 300
Explanation
The LCM of numbers 15,20,25 using the formula is 300. The above explained is how we ascertain it.
FAQs on LCM of 15,20 and 25
1.List the multiples of 15,20 and 25.
2.What is the LCM of 15,20 and 30?
3.What is the LCM of 12,15,20,22 and 25?
4. What is the LCM of 15,25 and 45?
5.What is the LCM of 20,25 and 30?
6.How can children in United Kingdom use numbers in everyday life to understand LCM of 15,20 and 25?
7.What are some fun ways kids in United Kingdom can practice LCM of 15,20 and 25 with numbers?
8.What role do numbers and LCM of 15,20 and 25 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve LCM of 15,20 and 25 skills?
Important glossaries for the LCM of 15,20 and 25
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.
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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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