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.
 

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
   

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.

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.

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.
 

• 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.