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128 LearnersLast updated on November 30th, 2024
LCM of 15 and 45
The LCM or Least Common Multiple of 15 and 45 is the smallest number which can be exactly divisible by each of 15 and 45. It can also be defined as the least number, which is a common multiple of all 15 and 45. LCM helps in scheduling, also used in traffic light mechanisms, etc.
What is the LCM of 15 and 45
The LCM of 15 and 45 is 45. So, 45 is the smallest multiple shared by the numbers 15 and 45. We can get the exact value of LCM of 15 and 45 through various methods. Let us see how.
How to find the LCM of 15 and 45
To find the LCM of 15 and 45 we will learn some methods:
- Listing Method
- Prime Factorization Method
- Division Method
LCM of 15 and 45 Using Listing the Multiples
Step 1:List down the multiples of each number
Multiples of 15 = 15,30,45,60,75,90,105,120,135,150,...
Multiples of 45= 45,90,135,180,225,315,....
Step 2: Find out the smallest multiple from the listed multiples
The smallest common multiple is 45
Thus, LCM (15,45) = 45.
LCM of 15 and 45 Using Prime Factorization
Rule: The prime factorization of each number is to be done, and then the highest power of the prime factors are multiplied to get the LCM.
Step 1: Find the prime factorization of the numbers:
Prime factorization of 15 = 3×5
Step 2: Take the highest powers of each prime factor, and multiply the highest powers to get the LCM:
LCM (15,45) = 45.
Prime factorization of 45 = 5×32
LCM of 15 and 45 Using Division Method
This is the most used method to find any LCM. It involves dividing both numbers 15 and 45 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. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers
The first common prime divisors for both 15 and 45 are 3 and 5. We choose 5.Step 2: Dividing 15 and 45 with 5, we get 3 and 9 respectively.
Step 3: Repeat Step 1 and 2 till both are getting perfectly divided. 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.
5×3×3 = 45
Thus, LCM (15,45) = 45
Common Mistakes and How to Avoid Them in LCM of 15 and 45
LCM of 15 and 45 Examples
Problem 1
The LCM of 15 and 45 is 45. Then what will be the LCM of 15 and 60?
Explanation
Problem 2
LCM (15,45) = x. Find the smallest positive integer (n), where n×x=90.
Explanation
Problem 3
What is the LCM of 12, 18 and 15?
Explanation
FAQs on LCM of 15 and 45
1.What is the LCM of 5 and 45?
2.What is the LCM of 12,15, and 45?
3.How to calculate LCM quickly?
4.How to calculate LCM?
5.What is the LCM of 20,25 and 30?
Important glossaries for the LCM of 15 and 45
- Prime Factor: A natural number or whole number which has factors that are 1 and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: numbers which have the only positive divisor of them both as 1.
- Relatively Prime Numbers: Numbers that have no common factors except 1.
- Multiples: The product we get when all the integers are multiplied with a particular number, one by one.
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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.
