LCM of 20 and 50
LCM of 20 and 50 is the smallest number among all common multiples of 20 and 50. The first few multiples of 20 and 50 are (20, 40, 60, 80, 100, 120, . . . ) and (50, 100, 150, 200, 250, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 50  by prime factorization, by listing multiples, and by division method.
1.  LCM of 20 and 50 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 20 and 50?
Answer: LCM of 20 and 50 is 100.
Explanation:
The LCM of two nonzero integers, x(20) and y(50), is the smallest positive integer m(100) that is divisible by both x(20) and y(50) without any remainder.
Methods to Find LCM of 20 and 50
Let's look at the different methods for finding the LCM of 20 and 50.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 20 and 50 by Prime Factorization
Prime factorization of 20 and 50 is (2 × 2 × 5) = 2^{2} × 5^{1} and (2 × 5 × 5) = 2^{1} × 5^{2} respectively. LCM of 20 and 50 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 5^{2} = 100.
Hence, the LCM of 20 and 50 by prime factorization is 100.
LCM of 20 and 50 by Division Method
To calculate the LCM of 20 and 50 by the division method, we will divide the numbers(20, 50) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 50.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 50. Write this prime number(2) on the left of the given numbers(20 and 50), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (20, 50) 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 20 and 50 is the product of all prime numbers on the left, i.e. LCM(20, 50) by division method = 2 × 2 × 5 × 5 = 100.
LCM of 20 and 50 by Listing Multiples
To calculate the LCM of 20 and 50 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 20 (20, 40, 60, 80, 100, 120, . . . ) and 50 (50, 100, 150, 200, 250, . . . . )
 Step 2: The common multiples from the multiples of 20 and 50 are 100, 200, . . .
 Step 3: The smallest common multiple of 20 and 50 is 100.
∴ The least common multiple of 20 and 50 = 100.
☛ Also Check:
 LCM of 4 and 24  24
 LCM of 2, 3, 4 and 5  60
 LCM of 3, 6 and 8  24
 LCM of 15 and 24  120
 LCM of 7 and 28  28
 LCM of 72 and 120  360
 LCM of 63 and 21  63
LCM of 20 and 50 Examples

Example 1: Find the smallest number that is divisible by 20 and 50 exactly.
Solution:
The smallest number that is divisible by 20 and 50 exactly is their LCM.
⇒ Multiples of 20 and 50: Multiples of 20 = 20, 40, 60, 80, 100, 120, . . . .
 Multiples of 50 = 50, 100, 150, 200, 250, 300, . . . .
Therefore, the LCM of 20 and 50 is 100.

Example 2: Verify the relationship between GCF and LCM of 20 and 50.
Solution:
The relation between GCF and LCM of 20 and 50 is given as,
LCM(20, 50) × GCF(20, 50) = Product of 20, 50
Prime factorization of 20 and 50 is given as, 20 = (2 × 2 × 5) = 2^{2} × 5^{1} and 50 = (2 × 5 × 5) = 2^{1} × 5^{2}
LCM(20, 50) = 100
GCF(20, 50) = 10
LHS = LCM(20, 50) × GCF(20, 50) = 100 × 10 = 1000
RHS = Product of 20, 50 = 20 × 50 = 1000
⇒ LHS = RHS = 1000
Hence, verified. 
Example 3: The product of two numbers is 1000. If their GCD is 10, what is their LCM?
Solution:
Given: GCD = 10
product of numbers = 1000
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1000/10
Therefore, the LCM is 100.
The probable combination for the given case is LCM(20, 50) = 100.
FAQs on LCM of 20 and 50
What is the LCM of 20 and 50?
The LCM of 20 and 50 is 100. To find the least common multiple (LCM) of 20 and 50, we need to find the multiples of 20 and 50 (multiples of 20 = 20, 40, 60, 80 . . . . 100; multiples of 50 = 50, 100, 150, 200) and choose the smallest multiple that is exactly divisible by 20 and 50, i.e., 100.
What are the Methods to Find LCM of 20 and 50?
The commonly used methods to find the LCM of 20 and 50 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
What is the Least Perfect Square Divisible by 20 and 50?
The least number divisible by 20 and 50 = LCM(20, 50)
LCM of 20 and 50 = 2 × 2 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 20 and 50 = 100 [Square root of 100 = √100 = ±10]
Therefore, 100 is the required number.
If the LCM of 50 and 20 is 100, Find its GCF.
LCM(50, 20) × GCF(50, 20) = 50 × 20
Since the LCM of 50 and 20 = 100
⇒ 100 × GCF(50, 20) = 1000
Therefore, the GCF = 1000/100 = 10.
What is the Relation Between GCF and LCM of 20, 50?
The following equation can be used to express the relation between GCF and LCM of 20 and 50, i.e. GCF × LCM = 20 × 50.
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