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163 LearnersLast updated on November 29th, 2024
LCM of 4 and 9
The Least common multiple (LCM) is the smallest number that is divisible by both 4 and 9. LCM can be solved using listing multiples method, prime factorization or division methods. Unknowingly, we use LCM in scheduling alarms for clocks or the movement of gears in cars.
What is the LCM of 4 and 9?
The LCM of 4 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 4 and 9?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 4 and 9 using the Listing Multiples Method
The LCM of 4 and 9 can be calculated using the following steps:
Step 1: Write down the multiples of each number
Multiples of 4 = 4,8,12,16,20,24,28,32,36,…
Multiples of 9 = 9,18,27,36,…
Step 2:Ascertain the smallest multiple from the listed multiples:
The smallest common multiple is 36.
Thus, LCM(4,9) = 36.
LCM of 4 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.
Step 1: Find the prime factors of each number:
Prime factorization of 4 = 2×2
Prime factorization of 9 = 3 × 3
Step 2:Take the highest powers of each prime factor =2×2×3×3
Step 3: Multiply the highest powers to get the LCM:
LCM(4, 9) =2×2×3×3 = 36.
LCM of 4 and 9 using the Division Method
This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.
Step 1: Write the numbers, divide by common prime factors and multiply the divisors.
Step 2: repeat untill we get 1 as remainder.
Thus, LCM(4, 9) = 36.
Common Mistakes and how to avoid them in LCM of 4 and 9
LCM of 4 and 9, examples
Problem 1
LCM of a and b is 36. a=4, find b.
Explanation
Problem 2
The LCM of a and b is 36 and their HCF is 1. Find their product.
Explanation
Problem 3
In a neighborhood park, the fountain show is turned on every 4 minutes, and the light show every 9 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?
Explanation
FAQs on LCM of 4 and 9
1.What is the LCM of 4,9 and 10?
2. What is the LCM of 4,9 and 11?
3.Are 4 and 9 co-prime numbers?
4.What is the HCF of 4 and 9?
5.What is the LCM of 4,7 and 9?
Important glossaries for the LCM of 4 and 9
- 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.
