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130 LearnersLast updated on January 22nd, 2025
LCM of 96 and 404
LCM is the smallest number that is common to all given numbers. LCM stands for least common multiple. LCM is used mostly for synchronizing repeating cycles such as putting alarm, following investments or for musical notes. Let us now learn about LCM of 96 and 404.
What is the LCM of 96 and 404?
The least common multiple of 96 and 404 is 9696. LCM has real-life applications like dividing items equally, arranging plants for gardening. It is also useful where events get repeated, example: Traffic lights
How to find LCM of 96 and 404?
There are many methods for identifying the LCM, let us not burden ourselves with all the methods. Let us learn only three popular and easy methods. Those are,
- Listing Multiples
- Prime factorization
- Division Methods
LCM of 96 and 404 using Listing multiples method
Listing multiple methods is easy to learn. Let us learn now
Multiples of 96: 96, 192, 288, 384, 480…….9696,
Multiples of 404: 404, 808, 1212, 1616, 2020, 2424, 2828, 3232, 3636, 4040, 4444, 4848, 5252, 5656, 6060, 6464, 6868, 7272, 7676, 8080, 8484, 8888, 9292, 9696, 10100, 10504
Among the list of multiples given above, we can see that 9696 is the common multiple. Therefore, LCM (96, 404) = 9696.
LCM of 96 and 404 using the Prime factorization method
Prime factorization is the method that break down any number into its prime factors. Here, we take the product of prime numbers with higher power to get the LCM. Follow the given steps to find the LCM of 96 and 404
The prime factorization of 96 = 25 x 31
The prime factorization of 404 = 22 x 1011
Now we will identify the prime factors with highest powers and take their product. Prime factors with the highest powers are 25, 31 and 1011
25 x 31 × 1011
32 × 3 x101 = 9696
Hence, LCM of 96 and 404 = 9696
LCM of 96 and 404 using the division method
In this method, we need to divide 96 and 404 with the common prime factor until we arrive at 1. Since children are reading it, it is important to break it into steps.
Step 1: The divisors must be placed on the left and the numbers on the right side
Step 2: Now we need to take 2 as the divisor, since the least common prime factor is 2 with which we are going to divide. Dividing with 2 get 48 and 202
Step 3: As both the numbers are divisible with 2 our divisor will be 2 again. Now by dividing 48, 202 by 2 we get at 24 and 101.
Step 4: It is important to remember in the division method that we need to divide until we get 1 as the remainder for both the numbers.
Common Mistakes in the LCM of 96 and 404
LCM of 96 and 404 practical Examples
Problem 1
If a bike passes on road A every 20 minutes and another bike passes on Road B every 30 minutes, when do both bikes pass on their respective roads at the same time?
Explanation
Problem 2
Assume two musical tones have a frequency of 96 and 404 Hz respectively. What is the lowest frequency where both the musical tone gets united to produce a melodious song?
Explanation
Problem 3
Task A is performed every 96 hours, whereas task B is performed every hour. When do both tasks are performed at the same time?
Explanation
Problem 4
If machine A stops functioning at 96 minutes and Machine B stops at 404 minutes, when do both machines stop functioning?
Explanation
Problem 5
If a vehicle is accelerating at 96 mph speed and the other vehicle at 404 mph speed, at what speed do both vehicles meet each other?
Explanation
FAQs on LCM of 96 and 404
1.What is the GCF of 96 and 404?
2.What is the LCM of 48 and 30?
3.Find the LCM of 32, 64, and 86 using the prime factorization method.
4.What is the prime factorization of 101?
5.What is the GCF of 56, 78?
Important Glossaries for the LCM of 96 and 404
- Factor: Numbers that can divide a given number, which leaves zero as the remainder. For example, the factors of the 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
- Prime factorization: The process of breaking down composite numbers into their prime factors. For example, the prime factorization of 100 is 22 × 52. From this we can say that the prime factors of 100 are 2 and 5.
- GCF: The greatest common factor is the largest number that can evenly divide two or more numbers. For example, the GCF of 96 and 404 is 4. That means, 4 is the biggest common factor that equally divided 96 and 404.
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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.
