LCM of 6 and 30
LCM of 6 and 30 is the smallest number among all common multiples of 6 and 30. The first few multiples of 6 and 30 are (6, 12, 18, 24, 30, 36, . . . ) and (30, 60, 90, 120, 150, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 30  by listing multiples, by prime factorization, and by division method.
1.  LCM of 6 and 30 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 6 and 30?
Answer: LCM of 6 and 30 is 30.
Explanation:
The LCM of two nonzero integers, x(6) and y(30), is the smallest positive integer m(30) that is divisible by both x(6) and y(30) without any remainder.
Methods to Find LCM of 6 and 30
Let's look at the different methods for finding the LCM of 6 and 30.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 6 and 30 by Division Method
To calculate the LCM of 6 and 30 by the division method, we will divide the numbers(6, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 30.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 30. Write this prime number(2) on the left of the given numbers(6 and 30), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (6, 30) 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 6 and 30 is the product of all prime numbers on the left, i.e. LCM(6, 30) by division method = 2 × 3 × 5 = 30.
LCM of 6 and 30 by Listing Multiples
To calculate the LCM of 6 and 30 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, . . . ) and 30 (30, 60, 90, 120, 150, 180, . . . . )
 Step 2: The common multiples from the multiples of 6 and 30 are 30, 60, . . .
 Step 3: The smallest common multiple of 6 and 30 is 30.
∴ The least common multiple of 6 and 30 = 30.
LCM of 6 and 30 by Prime Factorization
Prime factorization of 6 and 30 is (2 × 3) = 2^{1} × 3^{1} and (2 × 3 × 5) = 2^{1} × 3^{1} × 5^{1} respectively. LCM of 6 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 5^{1} = 30.
Hence, the LCM of 6 and 30 by prime factorization is 30.
☛ Also Check:
 LCM of 18, 24 and 30  360
 LCM of 20 and 30  60
 LCM of 2, 5 and 8  40
 LCM of 3 and 14  42
 LCM of 18 and 72  72
 LCM of 6 and 21  42
 LCM of 8, 9 and 12  72
LCM of 6 and 30 Examples

Example 1: Verify the relationship between GCF and LCM of 6 and 30.
Solution:
The relation between GCF and LCM of 6 and 30 is given as,
LCM(6, 30) × GCF(6, 30) = Product of 6, 30
Prime factorization of 6 and 30 is given as, 6 = (2 × 3) = 2^{1} × 3^{1} and 30 = (2 × 3 × 5) = 2^{1} × 3^{1} × 5^{1}
LCM(6, 30) = 30
GCF(6, 30) = 6
LHS = LCM(6, 30) × GCF(6, 30) = 30 × 6 = 180
RHS = Product of 6, 30 = 6 × 30 = 180
⇒ LHS = RHS = 180
Hence, verified. 
Example 2: The product of two numbers is 180. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 180
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 180/6
Therefore, the LCM is 30.
The probable combination for the given case is LCM(6, 30) = 30. 
Example 3: Find the smallest number that is divisible by 6 and 30 exactly.
Solution:
The smallest number that is divisible by 6 and 30 exactly is their LCM.
⇒ Multiples of 6 and 30: Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, . . . .
 Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, . . . .
Therefore, the LCM of 6 and 30 is 30.
FAQs on LCM of 6 and 30
What is the LCM of 6 and 30?
The LCM of 6 and 30 is 30. To find the least common multiple of 6 and 30, we need to find the multiples of 6 and 30 (multiples of 6 = 6, 12, 18, 24 . . . . 30; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 6 and 30, i.e., 30.
If the LCM of 30 and 6 is 30, Find its GCF.
LCM(30, 6) × GCF(30, 6) = 30 × 6
Since the LCM of 30 and 6 = 30
⇒ 30 × GCF(30, 6) = 180
Therefore, the GCF = 180/30 = 6.
What are the Methods to Find LCM of 6 and 30?
The commonly used methods to find the LCM of 6 and 30 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
What is the Least Perfect Square Divisible by 6 and 30?
The least number divisible by 6 and 30 = LCM(6, 30)
LCM of 6 and 30 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 6 and 30 = LCM(6, 30) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
How to Find the LCM of 6 and 30 by Prime Factorization?
To find the LCM of 6 and 30 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (30 = 2 × 3 × 5). LCM of 6 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 30.
⇒ LCM of 6, 30 = 2^{1} × 3^{1} × 5^{1} = 30.