LCM of 14 and 15
LCM of 14 and 15 is the smallest number among all common multiples of 14 and 15. The first few multiples of 14 and 15 are (14, 28, 42, 56, . . . ) and (15, 30, 45, 60, 75, 90, 105, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 15  by prime factorization, by listing multiples, and by division method.
1.  LCM of 14 and 15 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 14 and 15?
Answer: LCM of 14 and 15 is 210.
Explanation:
The LCM of two nonzero integers, x(14) and y(15), is the smallest positive integer m(210) that is divisible by both x(14) and y(15) without any remainder.
Methods to Find LCM of 14 and 15
The methods to find the LCM of 14 and 15 are explained below.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 14 and 15 by Listing Multiples
To calculate the LCM of 14 and 15 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 14 (14, 28, 42, 56, . . . ) and 15 (15, 30, 45, 60, 75, 90, 105, . . . . )
 Step 2: The common multiples from the multiples of 14 and 15 are 210, 420, . . .
 Step 3: The smallest common multiple of 14 and 15 is 210.
∴ The least common multiple of 14 and 15 = 210.
LCM of 14 and 15 by Division Method
To calculate the LCM of 14 and 15 by the division method, we will divide the numbers(14, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 15.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 15. Write this prime number(2) on the left of the given numbers(14 and 15), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (14, 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 14 and 15 is the product of all prime numbers on the left, i.e. LCM(14, 15) by division method = 2 × 3 × 5 × 7 = 210.
LCM of 14 and 15 by Prime Factorization
Prime factorization of 14 and 15 is (2 × 7) = 2^{1} × 7^{1} and (3 × 5) = 3^{1} × 5^{1} respectively. LCM of 14 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 5^{1} × 7^{1} = 210.
Hence, the LCM of 14 and 15 by prime factorization is 210.
☛ Also Check:
 LCM of 16, 28, 40 and 77  6160
 LCM of 15, 25, 40 and 75  600
 LCM of 12, 16, 24 and 36  144
 LCM of 12, 15, 20 and 54  540
 LCM of 12, 15, 20 and 27  540
 LCM of 12, 15, 18 and 27  540
 LCM of 10, 25, 35 and 40  1400
LCM of 14 and 15 Examples

Example 1: Find the smallest number that is divisible by 14 and 15 exactly.
Solution:
The smallest number that is divisible by 14 and 15 exactly is their LCM.
⇒ Multiples of 14 and 15: Multiples of 14 = 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, . . . .
 Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, . . . .
Therefore, the LCM of 14 and 15 is 210.

Example 2: The product of two numbers is 210. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 210
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 210/1
Therefore, the LCM is 210.
The probable combination for the given case is LCM(14, 15) = 210. 
Example 3: The GCD and LCM of two numbers are 1 and 210 respectively. If one number is 15, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 15 × a
⇒ a = (GCD × LCM)/15
⇒ a = (1 × 210)/15
⇒ a = 14
Therefore, the other number is 14.
FAQs on LCM of 14 and 15
What is the LCM of 14 and 15?
The LCM of 14 and 15 is 210. To find the least common multiple of 14 and 15, we need to find the multiples of 14 and 15 (multiples of 14 = 14, 28, 42, 56 . . . . 210; multiples of 15 = 15, 30, 45, 60 . . . . 210) and choose the smallest multiple that is exactly divisible by 14 and 15, i.e., 210.
What are the Methods to Find LCM of 14 and 15?
The commonly used methods to find the LCM of 14 and 15 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
What is the Least Perfect Square Divisible by 14 and 15?
The least number divisible by 14 and 15 = LCM(14, 15)
LCM of 14 and 15 = 2 × 3 × 5 × 7 [Incomplete pair(s): 2, 3, 5, 7]
⇒ Least perfect square divisible by each 14 and 15 = LCM(14, 15) × 2 × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210]
Therefore, 44100 is the required number.
Which of the following is the LCM of 14 and 15? 45, 210, 15, 16
The value of LCM of 14, 15 is the smallest common multiple of 14 and 15. The number satisfying the given condition is 210.
If the LCM of 15 and 14 is 210, Find its GCF.
LCM(15, 14) × GCF(15, 14) = 15 × 14
Since the LCM of 15 and 14 = 210
⇒ 210 × GCF(15, 14) = 210
Therefore, the greatest common factor = 210/210 = 1.
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