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LCM of 30 and 36

LCM of 30 and 36 is the smallest number among all common multiples of 30 and 36. The first few multiples of 30 and 36 are (30, 60, 90, 120, 150, 180, 210, . . . ) and (36, 72, 108, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 36 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 30 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 30 and 36?

Answer: LCM of 30 and 36 is 180.

Explanation:

The LCM of two non-zero integers, x(30) and y(36), is the smallest positive integer m(180) that is divisible by both x(30) and y(36) without any remainder.

Methods to Find LCM of 30 and 36

Let's look at the different methods for finding the LCM of 30 and 36.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 30 and 36 by Division Method

To calculate the LCM of 30 and 36 by the division method, we will divide the numbers(30, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 36.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 36. Write this prime number(2) on the left of the given numbers(30 and 36), separated as per the ladder arrangement.
Step 2: If any of the given numbers (30, 36) 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 30 and 36 is the product of all prime numbers on the left, i.e. LCM(30, 36) by division method = 2 × 2 × 3 × 3 × 5 = 180.

LCM of 30 and 36 by Listing Multiples

To calculate the LCM of 30 and 36 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 30 (30, 60, 90, 120, 150, 180, 210, . . . ) and 36 (36, 72, 108, 144, . . . . )
Step 2: The common multiples from the multiples of 30 and 36 are 180, 360, . . .
Step 3: The smallest common multiple of 30 and 36 is 180.

∴ The least common multiple of 30 and 36 = 180.

LCM of 30 and 36 by Prime Factorization

Prime factorization of 30 and 36 is (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 30 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 5¹ = 180.
Hence, the LCM of 30 and 36 by prime factorization is 180.

☛ Also Check:

LCM of 30 and 36 Examples

Example 1: The product of two numbers is 1080. If their GCD is 6, what is their LCM?

Solution:

Given: GCD = 6
product of numbers = 1080
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1080/6
Therefore, the LCM is 180.
The probable combination for the given case is LCM(30, 36) = 180.
Example 2: The GCD and LCM of two numbers are 6 and 180 respectively. If one number is 36, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 36 × m
⇒ m = (GCD × LCM)/36
⇒ m = (6 × 180)/36
⇒ m = 30
Therefore, the other number is 30.
Example 3: Verify the relationship between GCF and LCM of 30 and 36.

Solution:

The relation between GCF and LCM of 30 and 36 is given as,
LCM(30, 36) × GCF(30, 36) = Product of 30, 36
Prime factorization of 30 and 36 is given as, 30 = (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and 36 = (2 × 2 × 3 × 3) = 2² × 3²
LCM(30, 36) = 180
GCF(30, 36) = 6
LHS = LCM(30, 36) × GCF(30, 36) = 180 × 6 = 1080
RHS = Product of 30, 36 = 30 × 36 = 1080
⇒ LHS = RHS = 1080
Hence, verified.

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FAQs on LCM of 30 and 36

What is the LCM of 30 and 36?

The LCM of 30 and 36 is 180. To find the LCM of 30 and 36, we need to find the multiples of 30 and 36 (multiples of 30 = 30, 60, 90, 120 . . . . 180; multiples of 36 = 36, 72, 108, 144 . . . . 180) and choose the smallest multiple that is exactly divisible by 30 and 36, i.e., 180.

If the LCM of 36 and 30 is 180, Find its GCF.

LCM(36, 30) × GCF(36, 30) = 36 × 30
Since the LCM of 36 and 30 = 180
⇒ 180 × GCF(36, 30) = 1080
Therefore, the greatest common factor = 1080/180 = 6.

Which of the following is the LCM of 30 and 36? 11, 180, 3, 45

The value of LCM of 30, 36 is the smallest common multiple of 30 and 36. The number satisfying the given condition is 180.

What is the Least Perfect Square Divisible by 30 and 36?

The least number divisible by 30 and 36 = LCM(30, 36)
LCM of 30 and 36 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 30 and 36 = LCM(30, 36) × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

What are the Methods to Find LCM of 30 and 36?

The commonly used methods to find the LCM of 30 and 36 are:

Prime Factorization Method
Division Method
Listing Multiples

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