LCM of 50 and 60
LCM of 50 and 60 is the smallest number among all common multiples of 50 and 60. The first few multiples of 50 and 60 are (50, 100, 150, 200, . . . ) and (60, 120, 180, 240, 300, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 50 and 60  by division method, by listing multiples, and by prime factorization.
1.  LCM of 50 and 60 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 50 and 60?
Answer: LCM of 50 and 60 is 300.
Explanation:
The LCM of two nonzero integers, x(50) and y(60), is the smallest positive integer m(300) that is divisible by both x(50) and y(60) without any remainder.
Methods to Find LCM of 50 and 60
The methods to find the LCM of 50 and 60 are explained below.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 50 and 60 by Prime Factorization
Prime factorization of 50 and 60 is (2 × 5 × 5) = 2^{1} × 5^{2} and (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1} respectively. LCM of 50 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{1} × 5^{2} = 300.
Hence, the LCM of 50 and 60 by prime factorization is 300.
LCM of 50 and 60 by Division Method
To calculate the LCM of 50 and 60 by the division method, we will divide the numbers(50, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 50 and 60.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 50 and 60. Write this prime number(2) on the left of the given numbers(50 and 60), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (50, 60) 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 50 and 60 is the product of all prime numbers on the left, i.e. LCM(50, 60) by division method = 2 × 2 × 3 × 5 × 5 = 300.
LCM of 50 and 60 by Listing Multiples
To calculate the LCM of 50 and 60 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 50 (50, 100, 150, 200, . . . ) and 60 (60, 120, 180, 240, 300, 360, . . . . )
 Step 2: The common multiples from the multiples of 50 and 60 are 300, 600, . . .
 Step 3: The smallest common multiple of 50 and 60 is 300.
∴ The least common multiple of 50 and 60 = 300.
☛ Also Check:
 LCM of 4, 7 and 8  56
 LCM of 24 and 32  96
 LCM of 3 and 5  15
 LCM of 18 and 30  90
 LCM of 5 and 24  120
 LCM of 15 and 45  45
 LCM of 6 and 20  60
LCM of 50 and 60 Examples

Example 1: Verify the relationship between GCF and LCM of 50 and 60.
Solution:
The relation between GCF and LCM of 50 and 60 is given as,
LCM(50, 60) × GCF(50, 60) = Product of 50, 60
Prime factorization of 50 and 60 is given as, 50 = (2 × 5 × 5) = 2^{1} × 5^{2} and 60 = (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1}
LCM(50, 60) = 300
GCF(50, 60) = 10
LHS = LCM(50, 60) × GCF(50, 60) = 300 × 10 = 3000
RHS = Product of 50, 60 = 50 × 60 = 3000
⇒ LHS = RHS = 3000
Hence, verified. 
Example 2: Find the smallest number that is divisible by 50 and 60 exactly.
Solution:
The smallest number that is divisible by 50 and 60 exactly is their LCM.
⇒ Multiples of 50 and 60: Multiples of 50 = 50, 100, 150, 200, 250, 300, . . . .
 Multiples of 60 = 60, 120, 180, 240, 300, 360, . . . .
Therefore, the LCM of 50 and 60 is 300.

Example 3: The product of two numbers is 3000. If their GCD is 10, what is their LCM?
Solution:
Given: GCD = 10
product of numbers = 3000
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 3000/10
Therefore, the LCM is 300.
The probable combination for the given case is LCM(50, 60) = 300.
FAQs on LCM of 50 and 60
What is the LCM of 50 and 60?
The LCM of 50 and 60 is 300. To find the least common multiple (LCM) of 50 and 60, we need to find the multiples of 50 and 60 (multiples of 50 = 50, 100, 150, 200 . . . . 300; multiples of 60 = 60, 120, 180, 240 . . . . 300) and choose the smallest multiple that is exactly divisible by 50 and 60, i.e., 300.
If the LCM of 60 and 50 is 300, Find its GCF.
LCM(60, 50) × GCF(60, 50) = 60 × 50
Since the LCM of 60 and 50 = 300
⇒ 300 × GCF(60, 50) = 3000
Therefore, the greatest common factor = 3000/300 = 10.
How to Find the LCM of 50 and 60 by Prime Factorization?
To find the LCM of 50 and 60 using prime factorization, we will find the prime factors, (50 = 2 × 5 × 5) and (60 = 2 × 2 × 3 × 5). LCM of 50 and 60 is the product of prime factors raised to their respective highest exponent among the numbers 50 and 60.
⇒ LCM of 50, 60 = 2^{2} × 3^{1} × 5^{2} = 300.
What is the Relation Between GCF and LCM of 50, 60?
The following equation can be used to express the relation between GCF and LCM of 50 and 60, i.e. GCF × LCM = 50 × 60.
What are the Methods to Find LCM of 50 and 60?
The commonly used methods to find the LCM of 50 and 60 are:
 Listing Multiples
 Division Method
 Prime Factorization Method