321 LearnersLast updated on May 26th, 2025
LCM of 3 and 5
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3 and 5. 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 5?
The LCM of 3 and 5 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 3 and 5?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 3 and 5 using the Listing Multiples Method
The LCM of 3 and 5 can be found using the following steps:
Step 1: Write down the multiples of each number
Multiples of 3 = 3,6,9,12,15 …
Multiples of 5 = 5, 10,15,20 …
Step 2:Ascertain the smallest multiple from the listed multiples
The smallest common multiple is 15.
Thus, LCM(3, 5) = 15.
LCM of 3 and 5 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 3 = 3
Prime factorization of 5 = 5
Take the highest powers of each prime factor:
Highest power of 3 = 3
Highest power of 5 = 5
Multiply the highest powers to get the LCM:
LCM(3, 5) = 3 × 5 = 15
LCM of 3 and 5 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.
Step1: Write the numbers:
Step 2 : Divide by common prime factors and multiply the divisors:
3 × 5 = 15
Thus, LCM(3, 5) = 15.
Common Mistakes and how to avoid them while finding the LCM of 3 and 5
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3 and 5, make a note while practicing.
Mistake 1
Assuming LCM is always larger than both the numbers
In case of smaller numbers, it is commonly mistaken that their LCM is going to be larger than the both numbers, which is not always the case. To substantiate, the LCM of numbers 2 and 6 is 6, which is equal to the second number of the set and not larger as assumed. In the given case of 3 and 15, however, the LCM is larger than both numbers,15.
Mistake 2
Confusing between LCM and HCF of the numbers 3 and 5.
It is common for one to be confused between the HCF (Highest common factor) and LCM (least common multiple). LCM is the smallest number divisible by 2 and 6 while, the largest number that divides them both is the HCF.
A simple trick to remember is that the HCF is going to be a relatively smaller number than the LCM, as it deals with divisors.
Mistake 3
Not recognizing coprime Numbers
3 and 5 are coprime, i.e., they have no common factors other than 1 which leads to confusion about finding common multiples. Mistakenly, one may look for common factors when they realize there are none. In case of co prime numbers like 3 and 5, the LCM is the product of the numbers.
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LCM of 3 and 5, Examples
Problem 1
A number n is divisible by 3 and 5. The value of n is between 20 and 40, find n.
To solve for n, we first find the LCM of the numbers 3 and 5;
Prime factorization of 3 = 31
Prime factorization of 5 = 51
LCM (3,5) = 15
15×2 = 30, a multiple of both 3 and 5.
Explanation
We find a multiple of 15, that falls in the range of 20 and 40 is; 15 ×2 = 30, which is divisible by both 3 and 5.
Problem 2
Verify a×b = LCM (a,b) ×HCF(a,b) for 3 and 5.
a = 3, b= 5
a×b = LCM (a,b) ×HCF(a,b)
3×5 = LCM (3,5) ×HCF(3,5)
15 = 15 ×1
15 = 15
Explanation
LHS = RHS in the above solution, the relationship is hence verified.
Problem 3
The product of a and b is 45, and the HCF is 1. a = 3, find the LCM.
We know that; a×b = LCM (a,b) ×HCF(a,b)
Given; 3×b = 45, HCF(3,b)= 1
Applying the same in the formula;
45 = LCM (3,b) ×1
LCM (3,b) = 45/1 = 45
Now we solve for b - 3×b = 45
b = 45/3 = 15
Explanation
The other number is 15, LCM(3,15) = 15.
Problem 4
A car mechanic services a red car every 3 days and a blue car every 5 days. If the cars are serviced today, when will they be serviced next together?
The LCM of 3 and 5 is 15.
Explanation
Both cars will be serviced again in 15 days, which is the smallest time interval between the digits.
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FAQs on the LCM 3 and 5
1.What are the first two LCMs of the numbers 3 and 5 ?
2.What is the Least common denominator (LCD) of 3 and 5 ?
3.What do 3 and 5 have in common ?
4.What is the LCM of 3,5 and 7?
5.How to find multiples of 3 and 5 ?
6.How can children in United Kingdom use numbers in everyday life to understand LCM of 3 and 5?
7.What are some fun ways kids in United Kingdom can practice LCM of 3 and 5 with numbers?
8.What role do numbers and LCM of 3 and 5 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 3 and 5 skills?
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Important glossaries related to LCM of 3 and 5
- 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 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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