LCM of 10 and 15
LCM of 10 and 15 is the smallest number among all common multiples of 10 and 15. The first few multiples of 10 and 15 are (10, 20, 30, 40, 50, 60, 70, . . . ) and (15, 30, 45, 60, 75, 90, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 15  by prime factorization, by division method, and by listing multiples.
1.  LCM of 10 and 15 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 10 and 15?
Answer: LCM of 10 and 15 is 30.
Explanation:
The LCM of two nonzero integers, x(10) and y(15), is the smallest positive integer m(30) that is divisible by both x(10) and y(15) without any remainder.
Methods to Find LCM of 10 and 15
The methods to find the LCM of 10 and 15 are explained below.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 10 and 15 by Division Method
To calculate the LCM of 10 and 15 by the division method, we will divide the numbers(10, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 15.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 15. Write this prime number(2) on the left of the given numbers(10 and 15), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (10, 15) 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 15 is the product of all prime numbers on the left, i.e. LCM(10, 15) by division method = 2 × 3 × 5 = 30.
LCM of 10 and 15 by Listing Multiples
To calculate the LCM of 10 and 15 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 15 (15, 30, 45, 60, 75, 90, . . . . )
 Step 2: The common multiples from the multiples of 10 and 15 are 30, 60, . . .
 Step 3: The smallest common multiple of 10 and 15 is 30.
∴ The least common multiple of 10 and 15 = 30.
LCM of 10 and 15 by Prime Factorization
Prime factorization of 10 and 15 is (2 × 5) = 2^{1} × 5^{1} and (3 × 5) = 3^{1} × 5^{1} respectively. LCM of 10 and 15 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 15 by prime factorization is 30.
☛ Also Check:
 LCM of 72 and 108  216
 LCM of 70 and 90  630
 LCM of 7 and 9  63
 LCM of 7 and 8  56
 LCM of 7 and 7  7
 LCM of 7 and 56  56
 LCM of 7 and 49  49
LCM of 10 and 15 Examples

Example 1: Verify the relationship between GCF and LCM of 10 and 15.
Solution:
The relation between GCF and LCM of 10 and 15 is given as,
LCM(10, 15) × GCF(10, 15) = Product of 10, 15
Prime factorization of 10 and 15 is given as, 10 = (2 × 5) = 2^{1} × 5^{1} and 15 = (3 × 5) = 3^{1} × 5^{1}
LCM(10, 15) = 30
GCF(10, 15) = 5
LHS = LCM(10, 15) × GCF(10, 15) = 30 × 5 = 150
RHS = Product of 10, 15 = 10 × 15 = 150
⇒ LHS = RHS = 150
Hence, verified. 
Example 2: The product of two numbers is 150. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
product of numbers = 150
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 150/5
Therefore, the LCM is 30.
The probable combination for the given case is LCM(10, 15) = 30. 
Example 3: Find the smallest number that is divisible by 10 and 15 exactly.
Solution:
The smallest number that is divisible by 10 and 15 exactly is their LCM.
⇒ Multiples of 10 and 15: Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, . . . .
 Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, . . . .
Therefore, the LCM of 10 and 15 is 30.
FAQs on LCM of 10 and 15
What is the LCM of 10 and 15?
The LCM of 10 and 15 is 30. To find the least common multiple (LCM) of 10 and 15, we need to find the multiples of 10 and 15 (multiples of 10 = 10, 20, 30, 40; multiples of 15 = 15, 30, 45, 60) and choose the smallest multiple that is exactly divisible by 10 and 15, i.e., 30.
What is the Least Perfect Square Divisible by 10 and 15?
The least number divisible by 10 and 15 = LCM(10, 15)
LCM of 10 and 15 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 10 and 15 = LCM(10, 15) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
What is the Relation Between GCF and LCM of 10, 15?
The following equation can be used to express the relation between GCF and LCM of 10 and 15, i.e. GCF × LCM = 10 × 15.
If the LCM of 15 and 10 is 30, Find its GCF.
LCM(15, 10) × GCF(15, 10) = 15 × 10
Since the LCM of 15 and 10 = 30
⇒ 30 × GCF(15, 10) = 150
Therefore, the GCF (greatest common factor) = 150/30 = 5.
How to Find the LCM of 10 and 15 by Prime Factorization?
To find the LCM of 10 and 15 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (15 = 3 × 5). LCM of 10 and 15 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 15.
⇒ LCM of 10, 15 = 2^{1} × 3^{1} × 5^{1} = 30.
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