LCM of 6 and 10
LCM of 6 and 10 is the smallest number among all common multiples of 6 and 10. The first few multiples of 6 and 10 are (6, 12, 18, 24, 30, 36, 42, . . . ) and (10, 20, 30, 40, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 10  by listing multiples, by prime factorization, and by division method.
1.  LCM of 6 and 10 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 6 and 10?
Answer: LCM of 6 and 10 is 30.
Explanation:
The LCM of two nonzero integers, x(6) and y(10), is the smallest positive integer m(30) that is divisible by both x(6) and y(10) without any remainder.
Methods to Find LCM of 6 and 10
The methods to find the LCM of 6 and 10 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 6 and 10 by Division Method
To calculate the LCM of 6 and 10 by the division method, we will divide the numbers(6, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 10.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 10. Write this prime number(2) on the left of the given numbers(6 and 10), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (6, 10) 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 10 is the product of all prime numbers on the left, i.e. LCM(6, 10) by division method = 2 × 3 × 5 = 30.
LCM of 6 and 10 by Listing Multiples
To calculate the LCM of 6 and 10 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, 42, . . . ) and 10 (10, 20, 30, 40, . . . . )
 Step 2: The common multiples from the multiples of 6 and 10 are 30, 60, . . .
 Step 3: The smallest common multiple of 6 and 10 is 30.
∴ The least common multiple of 6 and 10 = 30.
LCM of 6 and 10 by Prime Factorization
Prime factorization of 6 and 10 is (2 × 3) = 2^{1} × 3^{1} and (2 × 5) = 2^{1} × 5^{1} respectively. LCM of 6 and 10 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 10 by prime factorization is 30.
☛ Also Check:
 LCM of 3, 6 and 12  12
 LCM of 28 and 30  420
 LCM of 7 and 11  77
 LCM of 21 and 24  168
 LCM of 5, 7 and 10  70
 LCM of 36 and 45  180
 LCM of 54 and 12  108
LCM of 6 and 10 Examples

Example 1: Find the smallest number that is divisible by 6 and 10 exactly.
Solution:
The smallest number that is divisible by 6 and 10 exactly is their LCM.
⇒ Multiples of 6 and 10: Multiples of 6 = 6, 12, 18, 24, 30, 36, . . . .
 Multiples of 10 = 10, 20, 30, 40, 50, 60, . . . .
Therefore, the LCM of 6 and 10 is 30.

Example 2: Verify the relationship between GCF and LCM of 6 and 10.
Solution:
The relation between GCF and LCM of 6 and 10 is given as,
LCM(6, 10) × GCF(6, 10) = Product of 6, 10
Prime factorization of 6 and 10 is given as, 6 = (2 × 3) = 2^{1} × 3^{1} and 10 = (2 × 5) = 2^{1} × 5^{1}
LCM(6, 10) = 30
GCF(6, 10) = 2
LHS = LCM(6, 10) × GCF(6, 10) = 30 × 2 = 60
RHS = Product of 6, 10 = 6 × 10 = 60
⇒ LHS = RHS = 60
Hence, verified. 
Example 3: The product of two numbers is 60. If their GCD is 2, what is their LCM?
Solution:
Given: GCD = 2
product of numbers = 60
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 60/2
Therefore, the LCM is 30.
The probable combination for the given case is LCM(6, 10) = 30.
FAQs on LCM of 6 and 10
What is the LCM of 6 and 10?
The LCM of 6 and 10 is 30. To find the LCM (least common multiple) of 6 and 10, we need to find the multiples of 6 and 10 (multiples of 6 = 6, 12, 18, 24 . . . . 30; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 6 and 10, i.e., 30.
What is the Least Perfect Square Divisible by 6 and 10?
The least number divisible by 6 and 10 = LCM(6, 10)
LCM of 6 and 10 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 6 and 10 = LCM(6, 10) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
If the LCM of 10 and 6 is 30, Find its GCF.
LCM(10, 6) × GCF(10, 6) = 10 × 6
Since the LCM of 10 and 6 = 30
⇒ 30 × GCF(10, 6) = 60
Therefore, the greatest common factor (GCF) = 60/30 = 2.
What is the Relation Between GCF and LCM of 6, 10?
The following equation can be used to express the relation between GCF and LCM of 6 and 10, i.e. GCF × LCM = 6 × 10.
Which of the following is the LCM of 6 and 10? 30, 42, 11, 5
The value of LCM of 6, 10 is the smallest common multiple of 6 and 10. The number satisfying the given condition is 30.