LCM of 8 and 20
LCM of 8 and 20 is the smallest number among all common multiples of 8 and 20. The first few multiples of 8 and 20 are (8, 16, 24, 32, . . . ) and (20, 40, 60, 80, 100, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 20  by prime factorization, by division method, and by listing multiples.
1.  LCM of 8 and 20 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 8 and 20?
Answer: LCM of 8 and 20 is 40.
Explanation:
The LCM of two nonzero integers, x(8) and y(20), is the smallest positive integer m(40) that is divisible by both x(8) and y(20) without any remainder.
Methods to Find LCM of 8 and 20
Let's look at the different methods for finding the LCM of 8 and 20.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 8 and 20 by Listing Multiples
To calculate the LCM of 8 and 20 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 8 (8, 16, 24, 32, . . . ) and 20 (20, 40, 60, 80, 100, . . . . )
 Step 2: The common multiples from the multiples of 8 and 20 are 40, 80, . . .
 Step 3: The smallest common multiple of 8 and 20 is 40.
∴ The least common multiple of 8 and 20 = 40.
LCM of 8 and 20 by Division Method
To calculate the LCM of 8 and 20 by the division method, we will divide the numbers(8, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 20.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 20. Write this prime number(2) on the left of the given numbers(8 and 20), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (8, 20) 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 8 and 20 is the product of all prime numbers on the left, i.e. LCM(8, 20) by division method = 2 × 2 × 2 × 5 = 40.
LCM of 8 and 20 by Prime Factorization
Prime factorization of 8 and 20 is (2 × 2 × 2) = 2^{3} and (2 × 2 × 5) = 2^{2} × 5^{1} respectively. LCM of 8 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 5^{1} = 40.
Hence, the LCM of 8 and 20 by prime factorization is 40.
☛ Also Check:
 LCM of 48, 56 and 72  1008
 LCM of 16, 24, 36 and 54  432
 LCM of 12, 18 and 20  180
 LCM of 9 and 21  63
 LCM of 3, 9 and 12  36
 LCM of 40 and 60  120
 LCM of 24 and 40  120
LCM of 8 and 20 Examples

Example 1: The product of two numbers is 160. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 160
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 160/4
Therefore, the LCM is 40.
The probable combination for the given case is LCM(8, 20) = 40. 
Example 2: The GCD and LCM of two numbers are 4 and 40 respectively. If one number is 20, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 20 × y
⇒ y = (GCD × LCM)/20
⇒ y = (4 × 40)/20
⇒ y = 8
Therefore, the other number is 8. 
Example 3: Verify the relationship between GCF and LCM of 8 and 20.
Solution:
The relation between GCF and LCM of 8 and 20 is given as,
LCM(8, 20) × GCF(8, 20) = Product of 8, 20
Prime factorization of 8 and 20 is given as, 8 = (2 × 2 × 2) = 2^{3} and 20 = (2 × 2 × 5) = 2^{2} × 5^{1}
LCM(8, 20) = 40
GCF(8, 20) = 4
LHS = LCM(8, 20) × GCF(8, 20) = 40 × 4 = 160
RHS = Product of 8, 20 = 8 × 20 = 160
⇒ LHS = RHS = 160
Hence, verified.
FAQs on LCM of 8 and 20
What is the LCM of 8 and 20?
The LCM of 8 and 20 is 40. To find the LCM of 8 and 20, we need to find the multiples of 8 and 20 (multiples of 8 = 8, 16, 24, 32 . . . . 40; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 8 and 20, i.e., 40.
What are the Methods to Find LCM of 8 and 20?
The commonly used methods to find the LCM of 8 and 20 are:
 Prime Factorization Method
 Division Method
 Listing Multiples
What is the Least Perfect Square Divisible by 8 and 20?
The least number divisible by 8 and 20 = LCM(8, 20)
LCM of 8 and 20 = 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 8 and 20 = LCM(8, 20) × 2 × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.
If the LCM of 20 and 8 is 40, Find its GCF.
LCM(20, 8) × GCF(20, 8) = 20 × 8
Since the LCM of 20 and 8 = 40
⇒ 40 × GCF(20, 8) = 160
Therefore, the GCF (greatest common factor) = 160/40 = 4.
How to Find the LCM of 8 and 20 by Prime Factorization?
To find the LCM of 8 and 20 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (20 = 2 × 2 × 5). LCM of 8 and 20 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 20.
⇒ LCM of 8, 20 = 2^{3} × 5^{1} = 40.
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