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LCM of 28, 36, 45, and 60

LCM of 28, 36, 45, and 60 is the smallest number among all common multiples of 28, 36, 45, and 60. The first few multiples of 28, 36, 45, and 60 are (28, 56, 84, 112, 140 . . .), (36, 72, 108, 144, 180 . . .), (45, 90, 135, 180, 225 . . .), and (60, 120, 180, 240, 300 . . .) respectively. There are 3 commonly used methods to find LCM of 28, 36, 45, 60 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 28, 36, 45, and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 28, 36, 45, and 60?

Answer: LCM of 28, 36, 45, and 60 is 1260.

Explanation:

The LCM of four non-zero integers, a(28), b(36), c(45), and d(60), is the smallest positive integer m(1260) that is divisible by a(28), b(36), c(45), and d(60) without any remainder.

Methods to Find LCM of 28, 36, 45, and 60

Let's look at the different methods for finding the LCM of 28, 36, 45, and 60.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 28, 36, 45, and 60 by Prime Factorization

Prime factorization of 28, 36, 45, and 60 is (2 × 2 × 7) = 2² × 7¹, (2 × 2 × 3 × 3) = 2² × 3², (3 × 3 × 5) = 3² × 5¹, and (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ respectively. LCM of 28, 36, 45, and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 5¹ × 7¹ = 1260.
Hence, the LCM of 28, 36, 45, and 60 by prime factorization is 1260.

LCM of 28, 36, 45, and 60 by Listing Multiples

To calculate the LCM of 28, 36, 45, 60 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 28 (28, 56, 84, 112, 140 . . .), 36 (36, 72, 108, 144, 180 . . .), 45 (45, 90, 135, 180, 225 . . .), and 60 (60, 120, 180, 240, 300 . . .).
Step 2: The common multiples from the multiples of 28, 36, 45, and 60 are 1260, 2520, . . .
Step 3: The smallest common multiple of 28, 36, 45, and 60 is 1260.

∴ The least common multiple of 28, 36, 45, and 60 = 1260.

LCM of 28, 36, 45, and 60 by Division Method

To calculate the LCM of 28, 36, 45, and 60 by the division method, we will divide the numbers(28, 36, 45, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 28, 36, 45, and 60.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 28, 36, 45, and 60. Write this prime number(2) on the left of the given numbers(28, 36, 45, and 60), separated as per the ladder arrangement.
Step 2: If any of the given numbers (28, 36, 45, 60) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 28, 36, 45, and 60 is the product of all prime numbers on the left, i.e. LCM(28, 36, 45, 60) by division method = 2 × 2 × 3 × 3 × 5 × 7 = 1260.

☛ Also Check:

LCM of 28, 36, 45, and 60 Examples

Example 1: Find the smallest number which when divided by 28, 36, 45, and 60 leaves 18 as the remainder in each case.

Solution:

The smallest number exactly divisible by 28, 36, 45, and 60 = LCM(28, 36, 45, 60) ⇒ Smallest number which leaves 18 as remainder when divided by 28, 36, 45, and 60 = LCM(28, 36, 45, 60) + 18
- 28 = 2² × 7¹
- 36 = 2² × 3²
- 45 = 3² × 5¹
- 60 = 2² × 3¹ × 5¹
LCM(28, 36, 45, 60) = 2² × 3² × 5¹ × 7¹ = 1260
⇒ The required number = 1260 + 18 = 1278.
Example 2: Find the smallest number that is divisible by 28, 36, 45, 60 exactly.

Solution:

The value of LCM(28, 36, 45, 60) will be the smallest number that is exactly divisible by 28, 36, 45, and 60.
⇒ Multiples of 28, 36, 45, and 60:
- Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, . . . ., 1204, 1232, 1260, . . . .
- Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . ., 1116, 1152, 1188, 1224, 1260, . . . .
- Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, . . . ., 1080, 1125, 1170, 1215, 1260, . . . .
- Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, . . . ., 1140, 1200, 1260, . . . .
Therefore, the LCM of 28, 36, 45, and 60 is 1260.
Example 3: Which of the following is the LCM of 28, 36, 45, 60? 1260, 25, 52, 45.

Solution:

The value of LCM of 28, 36, 45, and 60 is the smallest common multiple of 28, 36, 45, and 60. The number satisfying the given condition is 1260. ∴LCM(28, 36, 45, 60) = 1260.

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FAQs on LCM of 28, 36, 45, and 60

What is the LCM of 28, 36, 45, and 60?

The LCM of 28, 36, 45, and 60 is 1260. To find the LCM of 28, 36, 45, and 60, we need to find the multiples of 28, 36, 45, and 60 (multiples of 28 = 28, 56, 84, 112 . . . . 1260 . . . . ; multiples of 36 = 36, 72, 108, 144 . . . . 1260 . . . . ; multiples of 45 = 45, 90, 135, 180 . . . . 1260 . . . . ; multiples of 60 = 60, 120, 180, 240 . . . . 1260 . . . . ) and choose the smallest multiple that is exactly divisible by 28, 36, 45, and 60, i.e., 1260.

What are the Methods to Find LCM of 28, 36, 45, 60?

The commonly used methods to find the LCM of 28, 36, 45, 60 are:

Division Method
Prime Factorization Method
Listing Multiples

How to Find the LCM of 28, 36, 45, and 60 by Prime Factorization?

To find the LCM of 28, 36, 45, and 60 using prime factorization, we will find the prime factors, (28 = 2² × 7¹), (36 = 2² × 3²), (45 = 3² × 5¹), and (60 = 2² × 3¹ × 5¹). LCM of 28, 36, 45, and 60 is the product of prime factors raised to their respective highest exponent among the numbers 28, 36, 45, and 60.
⇒ LCM of 28, 36, 45, 60 = 2² × 3² × 5¹ × 7¹ = 1260.

Which of the following is the LCM of 28, 36, 45, and 60? 3, 2, 1260, 105

The value of LCM of 28, 36, 45, 60 is the smallest common multiple of 28, 36, 45, and 60. The number satisfying the given condition is 1260.

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