LCM of 50 and 75
LCM of 50 and 75 is the smallest number among all common multiples of 50 and 75. The first few multiples of 50 and 75 are (50, 100, 150, 200, 250, 300, 350, . . . ) and (75, 150, 225, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 50 and 75  by listing multiples, by division method, and by prime factorization.
1.  LCM of 50 and 75 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 50 and 75?
Answer: LCM of 50 and 75 is 150.
Explanation:
The LCM of two nonzero integers, x(50) and y(75), is the smallest positive integer m(150) that is divisible by both x(50) and y(75) without any remainder.
Methods to Find LCM of 50 and 75
The methods to find the LCM of 50 and 75 are explained below.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 50 and 75 by Listing Multiples
To calculate the LCM of 50 and 75 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, 250, 300, 350, . . . ) and 75 (75, 150, 225, 300, . . . . )
 Step 2: The common multiples from the multiples of 50 and 75 are 150, 300, . . .
 Step 3: The smallest common multiple of 50 and 75 is 150.
∴ The least common multiple of 50 and 75 = 150.
LCM of 50 and 75 by Division Method
To calculate the LCM of 50 and 75 by the division method, we will divide the numbers(50, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 50 and 75.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 50 and 75. Write this prime number(2) on the left of the given numbers(50 and 75), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (50, 75) 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 75 is the product of all prime numbers on the left, i.e. LCM(50, 75) by division method = 2 × 3 × 5 × 5 = 150.
LCM of 50 and 75 by Prime Factorization
Prime factorization of 50 and 75 is (2 × 5 × 5) = 2^{1} × 5^{2} and (3 × 5 × 5) = 3^{1} × 5^{2} respectively. LCM of 50 and 75 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 5^{2} = 150.
Hence, the LCM of 50 and 75 by prime factorization is 150.
☛ Also Check:
 LCM of 2, 5 and 8  40
 LCM of 11 and 12  132
 LCM of 63 and 105  315
 LCM of 25 and 36  900
 LCM of 16 and 30  240
 LCM of 14 and 22  154
 LCM of 36 and 72  72
LCM of 50 and 75 Examples

Example 1: The GCD and LCM of two numbers are 25 and 150 respectively. If one number is 50, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 50 × p
⇒ p = (GCD × LCM)/50
⇒ p = (25 × 150)/50
⇒ p = 75
Therefore, the other number is 75. 
Example 2: Find the smallest number that is divisible by 50 and 75 exactly.
Solution:
The smallest number that is divisible by 50 and 75 exactly is their LCM.
⇒ Multiples of 50 and 75: Multiples of 50 = 50, 100, 150, 200, 250, 300, 350, . . . .
 Multiples of 75 = 75, 150, 225, 300, 375, 450, 525, . . . .
Therefore, the LCM of 50 and 75 is 150.

Example 3: The product of two numbers is 3750. If their GCD is 25, what is their LCM?
Solution:
Given: GCD = 25
product of numbers = 3750
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 3750/25
Therefore, the LCM is 150.
The probable combination for the given case is LCM(50, 75) = 150.
FAQs on LCM of 50 and 75
What is the LCM of 50 and 75?
The LCM of 50 and 75 is 150. To find the least common multiple of 50 and 75, we need to find the multiples of 50 and 75 (multiples of 50 = 50, 100, 150, 200; multiples of 75 = 75, 150, 225, 300) and choose the smallest multiple that is exactly divisible by 50 and 75, i.e., 150.
How to Find the LCM of 50 and 75 by Prime Factorization?
To find the LCM of 50 and 75 using prime factorization, we will find the prime factors, (50 = 2 × 5 × 5) and (75 = 3 × 5 × 5). LCM of 50 and 75 is the product of prime factors raised to their respective highest exponent among the numbers 50 and 75.
⇒ LCM of 50, 75 = 2^{1} × 3^{1} × 5^{2} = 150.
What is the Relation Between GCF and LCM of 50, 75?
The following equation can be used to express the relation between GCF and LCM of 50 and 75, i.e. GCF × LCM = 50 × 75.
What are the Methods to Find LCM of 50 and 75?
The commonly used methods to find the LCM of 50 and 75 are:
 Prime Factorization Method
 Listing Multiples
 Division Method
If the LCM of 75 and 50 is 150, Find its GCF.
LCM(75, 50) × GCF(75, 50) = 75 × 50
Since the LCM of 75 and 50 = 150
⇒ 150 × GCF(75, 50) = 3750
Therefore, the GCF (greatest common factor) = 3750/150 = 25.
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