LCM of 10 and 30
LCM of 10 and 30 is the smallest number among all common multiples of 10 and 30. The first few multiples of 10 and 30 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (30, 60, 90, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 30  by prime factorization, by division method, and by listing multiples.
1.  LCM of 10 and 30 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 10 and 30?
Answer: LCM of 10 and 30 is 30.
Explanation:
The LCM of two nonzero integers, x(10) and y(30), is the smallest positive integer m(30) that is divisible by both x(10) and y(30) without any remainder.
Methods to Find LCM of 10 and 30
Let's look at the different methods for finding the LCM of 10 and 30.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 10 and 30 by Prime Factorization
Prime factorization of 10 and 30 is (2 × 5) = 2^{1} × 5^{1} and (2 × 3 × 5) = 2^{1} × 3^{1} × 5^{1} respectively. LCM of 10 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 10 and 30 by prime factorization is 30.
LCM of 10 and 30 by Listing Multiples
To calculate the LCM of 10 and 30 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, 60, 70, . . . ) and 30 (30, 60, 90, 120, . . . . )
 Step 2: The common multiples from the multiples of 10 and 30 are 30, 60, . . .
 Step 3: The smallest common multiple of 10 and 30 is 30.
∴ The least common multiple of 10 and 30 = 30.
LCM of 10 and 30 by Division Method
To calculate the LCM of 10 and 30 by the division method, we will divide the numbers(10, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 30.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 30. Write this prime number(2) on the left of the given numbers(10 and 30), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (10, 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 10 and 30 is the product of all prime numbers on the left, i.e. LCM(10, 30) by division method = 2 × 3 × 5 = 30.
☛ Also Check:
 LCM of 54 and 90  270
 LCM of 54 and 72  216
 LCM of 54 and 60  540
 LCM of 54 and 27  54
 LCM of 520 and 468  4680
 LCM of 50 and 75  150
 LCM of 50 and 60  300
LCM of 10 and 30 Examples

Example 1: The GCD and LCM of two numbers are 10 and 30 respectively. If one number is 10, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 10 × p
⇒ p = (GCD × LCM)/10
⇒ p = (10 × 30)/10
⇒ p = 30
Therefore, the other number is 30. 
Example 2: The product of two numbers is 300. If their GCD is 10, what is their LCM?
Solution:
Given: GCD = 10
product of numbers = 300
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 300/10
Therefore, the LCM is 30.
The probable combination for the given case is LCM(10, 30) = 30. 
Example 3: Find the smallest number that is divisible by 10 and 30 exactly.
Solution:
The smallest number that is divisible by 10 and 30 exactly is their LCM.
⇒ Multiples of 10 and 30: Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, . . . .
 Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, . . . .
Therefore, the LCM of 10 and 30 is 30.
FAQs on LCM of 10 and 30
What is the LCM of 10 and 30?
The LCM of 10 and 30 is 30. To find the LCM (least common multiple) of 10 and 30, we need to find the multiples of 10 and 30 (multiples of 10 = 10, 20, 30, 40; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 10 and 30, i.e., 30.
How to Find the LCM of 10 and 30 by Prime Factorization?
To find the LCM of 10 and 30 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (30 = 2 × 3 × 5). LCM of 10 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 30.
⇒ LCM of 10, 30 = 2^{1} × 3^{1} × 5^{1} = 30.
Which of the following is the LCM of 10 and 30? 40, 5, 28, 30
The value of LCM of 10, 30 is the smallest common multiple of 10 and 30. The number satisfying the given condition is 30.
What are the Methods to Find LCM of 10 and 30?
The commonly used methods to find the LCM of 10 and 30 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
If the LCM of 30 and 10 is 30, Find its GCF.
LCM(30, 10) × GCF(30, 10) = 30 × 10
Since the LCM of 30 and 10 = 30
⇒ 30 × GCF(30, 10) = 300
Therefore, the greatest common factor (GCF) = 300/30 = 10.
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