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205 LearnersLast updated on November 29th, 2024
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.
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
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.
Explanation
Problem 2
Verify a×b = LCM (a,b) ×HCF(a,b) for 3 and 5.
Explanation
Problem 3
The product of a and b is 45, and the HCF is 1. a = 3, find the LCM.
Explanation
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?
Explanation
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 ?
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
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.
