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188 LearnersLast updated on December 2nd, 2024
LCM of 5 and 9
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 5 and 9. 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 5 and 9?
The LCM of 5 and 9 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 5 and 9?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 5 and 9 using the Listing Multiples Method
The LCM of 5 and 9 can be found using the following steps:
Step 1: Write down the multiples of each number
Multiples of 5 = 5,10,15,20,25,30,35,40,45,…
Multiples of 9 = 9, 18, 27, 36,45,54, …
Step 2:Ascertain the smallest multiple from the listed multiples
The least common multiple is 45.
LCM of 5 and 9 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.
Step1: Find the prime factors of the numbers
Prime factorization of 5 = 5
Prime factorization of 9 = 3 × 3
Step2: Take the highest powers of each prime factor
Highest power of 5 = 5
Highest power of 9 = 32
Step3 : Multiply the highest powers to get the LCM:
LCM(5, 9) = 5×32 = 45
LCM of 5 and 9 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 : keep dividing till we get 1 as remainder.
5 × 3 × 3 = 45
Thus, LCM(5, 9) = 45
Common Mistakes and how to avoid them in LCM of 5 and 9
LCM of 5 and 9, Examples
Problem 1
LCM of a and b is 45. a=5, find b.
Explanation
Problem 2
LCM(a,b)×HCF(a,b) = a×b, verify the relationship between the HCF and LCM of 5 and 9 using the given formula.
Explanation
Problem 3
A yellow bulb is replaced every 5 months and a white bulb is replaced every 9 months. If both of them are replaced today, after how many months will they need to be replaced?
Explanation
FAQs on LCM of 5 and 9
1.What is the LCD (Lowest common denominator) of 5 and 9?
2.What is the LCM of 7,5 and 9?
3.What is the LCM of 9,5 and 18?
4.What is the LCM of 5,9 and 12 ?
5.What is the HCF of 5 and 9?
Important glossaries for LCM of 5 and 9
- 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.
