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121 LearnersLast updated on January 21st, 2025
LCM of 28, 36, 45 and 60
LCM is the smallest number that is a common multiple of two or more numbers. LCM helps in making machines works by matching their gears, so they can move together at the same time, and it also helps to plan repeated tasks. We will learn here the LCM of 28, 36, 45 and 60.
What is the LCM of 28, 36, 45 and 60
The least common multiple of 28, 36, 45 and 60 is 1260. This is the smallest positive number, which is a common multiple of the numbers given. The LCM of any number is always positive. If both the numbers are co-primes, their LCM is the product of those two numbers.
How to find the LCM of 28, 36, 45 and 60
There are several methods to find the LCM of 28, 36, 45 and 60. The following are the methods to find LCM:
- Listing Multiples
- Prime Factorization
- Division Method
LCM of 28, 36, 45 and 60 Using Listing Multiples Method
Listing multiples method involves writing the multiples of each number and identifying the smallest common multiple.
- Let us find LCM of 28, 36, 45 and 60 using this method.
- In this method, we have to list multiples of all the given numbers.
- Identify the common multiples among all the multiples
Find the least common multiple
Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308, 336, 364, 392, 420, 448, 476, 504, 532, 560, 588, 616, 644, 672, 700, 728, 756, 784, 812, 840, 868, 896, 924, 952, 980, 1008, 1036, 1064, 1092, 1120, 1148, 1176, 1204, 1232,1260.
Multiples of 36 = 36, 72, 108, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972, 1008, 1044, 1080, 1116, 1152,1188, 1224, 1260.
Multiples of 45 = 45, 90, 135, 225, 270, 315, 360, 405, 450, 495, 540, 585, 630, 675, 720, 765, 810, 855, 900, 945, 990, 1035, 1080, 1125, 1170, 1215, 1260.
Multiples of 60 = 60,120,180,240,300,360,420,480,540,600,660,720,780,840,900,960,1020,1080, 1140, 1200, 1260.
1260 is the only common number among all the multiples of 28, 36, 45 and 60 and the smallest common multiple is 1260.
LCM of 28, 36, 45 and 60 using Prime Factorization
To find the LCM of 28, 36, 45 and 60 using the prime factorization method, follow these steps mentioned below:
Step1: Find the prime factorization of each number
28 = 22 x 7
36 = 22 x 32
45 = 32 x 5
60 = 22 x 3 x 5
Step2: Identify all the prime factors
The prime factors among all the numbers are 2, 3, 5, 7
Step3: Among all the prime factors, take the highest power of each prime factor
Highest power of 2 is 22
Highest power of 3 is 32
Highest power of 5 is 51
Highest power of 7 is 71
Step4: Multiply the highest powers together to find the LCM
LCM = 22 x 32 x 51 x 71
LCM = 4 x 9 x 5 x 7
LCM = 1260.
The LCM of 28, 36, 45 and 60 is 1260.
LCM of 28, 36, 45 and 60 using the Division Method
In the division method, first divide the numbers by the smallest prime number that divides at least one number. Continue dividing the resultant numbers by prime numbers until all reduces to 1. The LCM of the numbers will be the product of all prime numbers which you used as divisors. Let us know the step-by-step process to find the LCM of 28, 36, 45 and 60.
Step1: The numbers 28, 36, 45 and 60 should be divided by 2.
Step2: After dividing, we get 14, 18, 45 and 30. We continue the division by 2.
Step3: We get 7, 9, 45 and 15. Division is repeated with 3.
Step4: We get 7, 3, 15 and 5. Division is continued with 3.
Step5: We get 7, 1, 5 and 5. Division is repeated with 5.
Step6: We get 7, 1, 1 and 1. Divide them with 7.
Step7: The remainder will be 1, 1, 1 and 1.
The LCM of 28, 36, 45 and 60 is 2 x 2 x 3 x 3 x 5 x 7 = 1260.
Common Mistakes and How to Avoid Them in LCM of 28, 36, 45 and 60
LCM of 28, 36, 45 and 60 Examples
Problem 1
A factory has four machines that operate on cycles of 28 seconds, 36 seconds, 45 seconds, and 60 seconds. If all the machines start a new cycle at the same time, how long will it take before they all start a cycle together again?
Explanation
Problem 2
In a school: Bell A rings every 28 minutes. Bell B rings every 36 minutes. Bell C rings every 45 minutes. Bell D rings every 60 minutes. If all the bells ring together at 8:00 AM, when will they ring together next?
Explanation
Problem 3
Four frogs jump at intervals of 28 seconds, 36 seconds, 45 seconds and 60 seconds. If they all jump together now, how many seconds will pass before they jump together again?
Explanation
Problem 4
Three swings move at intervals of 28 seconds, 36 seconds, and 60 seconds. If they all move together now, when will they move together again?
Explanation
FAQs on Least Common Multiple of 28, 36, 45 and 60
1.Is 1260 divisible by 28, 36, 45 and 60?
2.What are the first three common multiples of 28, 36, 45 and 60?
3.What is the LCM of 28 and 36?
4.What is the prime factorization of 28?
5.What are the prime factors of 28?
Important Glossaries for LCM of 28, 36, 45 and 60
- Prime numbers: The numbers which do not have more than two factors, except 1 and itself For example: 2 is a prime number.
- Multiples: A multiple of a number is the product of that number and a whole number.Example: 28 is a multiple of 4.
- Prime Factorization: It is the process of expressing a number as the product of its prime factors.
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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.
