156 LearnersLast updated on May 26th, 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
When students are learning how to find the LCM, they might make some mistakes. Here are a few mistakes made by students and how to avoid them
Mistake 1
Using Non-prime divisors
Students sometimes try to divide by numbers which are not prime, like they may divide with 4 or 6. To avoid this, they should know we are supposed to use prime numbers to divide numbers in division method.
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?
To solve this, first find the LCM of 28, 36, 45 and 60.
LCM = 22 x 32 x 5 x 7 = 1260 seconds.
1260 seconds = 21 minutes.
Explanation
The machines in the factory operates on cycles of 28, 36, 45 and 60 seconds. The LCM of 28, 36, 45 and 60 is 1260. All the machines will start a cycle together after 1260 seconds, which is 21 minutes.
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?
LCM of 28. 36, 45 and 60
LCM = 22 x 32 x 5 x 7 = 1260 minutes.
Convert the 1260 minutes to hours = 1260 ÷ 60 = 21 hours
8:00 AM+ 21 hours = 5:00 AM(next day)
Explanation
Four bells A, B, C, D ring every 28, 36, 45 and 60 minutes respectively. LCM of 28, 36, 45 and 60 is 1260. The bells will ring together after 1260 minutes. Convert 1260 minutes to hours, which is 21 hours. Again, they all will ring together at 5:00am the next day.
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?
Find the LCM of 28, 36, 45 and 60.
LCM = 22 x 32 x 5 x 7 = 1260 seconds
1260 ÷ 60 = 21 minutes.
Explanation
Find the LCM of 28, 36, 4 and 60 which is 1260. Four frogs will jump together after 1260 seconds. Convert 1260 seconds to minutes by dividing with 60. After 21 minutes, they will jump together again.
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?
LCM of 28, 36 and 60
LCM = 22 x 32 x 5 x 7 = 1260 seconds.
The swings will move together after 1260 seconds.
Explanation
The LCM of 28, 36 and 60 is 1260. The swings will start moving together after 1260 seconds.
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?
6.How can children in Indonesia use numbers in everyday life to understand LCM of 28, 36, 45 and 60?
7.What are some fun ways kids in Indonesia can practice LCM of 28, 36, 45 and 60 with numbers?
8.What role do numbers and LCM of 28, 36, 45 and 60 play in helping children in Indonesia develop problem-solving skills?
9.How can families in Indonesia create number-rich environments to improve LCM of 28, 36, 45 and 60 skills?
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.
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