LCM of 20 and 45
LCM of 20 and 45 is the smallest number among all common multiples of 20 and 45. The first few multiples of 20 and 45 are (20, 40, 60, 80, 100, . . . ) and (45, 90, 135, 180, 225, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 45  by division method, by prime factorization, and by listing multiples.
1.  LCM of 20 and 45 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 20 and 45?
Answer: LCM of 20 and 45 is 180.
Explanation:
The LCM of two nonzero integers, x(20) and y(45), is the smallest positive integer m(180) that is divisible by both x(20) and y(45) without any remainder.
Methods to Find LCM of 20 and 45
Let's look at the different methods for finding the LCM of 20 and 45.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 20 and 45 by Division Method
To calculate the LCM of 20 and 45 by the division method, we will divide the numbers(20, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 45.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 45. Write this prime number(2) on the left of the given numbers(20 and 45), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (20, 45) 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 45 is the product of all prime numbers on the left, i.e. LCM(20, 45) by division method = 2 × 2 × 3 × 3 × 5 = 180.
LCM of 20 and 45 by Prime Factorization
Prime factorization of 20 and 45 is (2 × 2 × 5) = 2^{2} × 5^{1} and (3 × 3 × 5) = 3^{2} × 5^{1} respectively. LCM of 20 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{2} × 5^{1} = 180.
Hence, the LCM of 20 and 45 by prime factorization is 180.
LCM of 20 and 45 by Listing Multiples
To calculate the LCM of 20 and 45 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, . . . ) and 45 (45, 90, 135, 180, 225, . . . . )
 Step 2: The common multiples from the multiples of 20 and 45 are 180, 360, . . .
 Step 3: The smallest common multiple of 20 and 45 is 180.
∴ The least common multiple of 20 and 45 = 180.
☛ Also Check:
 LCM of 2 and 13  26
 LCM of 4, 12 and 16  48
 LCM of 2 and 4  4
 LCM of 56 and 70  280
 LCM of 40 and 56  280
 LCM of 60 and 84  420
 LCM of 12 and 27  108
LCM of 20 and 45 Examples

Example 1: The product of two numbers is 900. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
product of numbers = 900
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 900/5
Therefore, the LCM is 180.
The probable combination for the given case is LCM(20, 45) = 180. 
Example 2: Find the smallest number that is divisible by 20 and 45 exactly.
Solution:
The smallest number that is divisible by 20 and 45 exactly is their LCM.
⇒ Multiples of 20 and 45: Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, . . . .
 Multiples of 45 = 45, 90, 135, 180, 225, 270, . . . .
Therefore, the LCM of 20 and 45 is 180.

Example 3: Verify the relationship between GCF and LCM of 20 and 45.
Solution:
The relation between GCF and LCM of 20 and 45 is given as,
LCM(20, 45) × GCF(20, 45) = Product of 20, 45
Prime factorization of 20 and 45 is given as, 20 = (2 × 2 × 5) = 2^{2} × 5^{1} and 45 = (3 × 3 × 5) = 3^{2} × 5^{1}
LCM(20, 45) = 180
GCF(20, 45) = 5
LHS = LCM(20, 45) × GCF(20, 45) = 180 × 5 = 900
RHS = Product of 20, 45 = 20 × 45 = 900
⇒ LHS = RHS = 900
Hence, verified.
FAQs on LCM of 20 and 45
What is the LCM of 20 and 45?
The LCM of 20 and 45 is 180. To find the least common multiple (LCM) of 20 and 45, we need to find the multiples of 20 and 45 (multiples of 20 = 20, 40, 60, 80 . . . . 180; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 20 and 45, i.e., 180.
If the LCM of 45 and 20 is 180, Find its GCF.
LCM(45, 20) × GCF(45, 20) = 45 × 20
Since the LCM of 45 and 20 = 180
⇒ 180 × GCF(45, 20) = 900
Therefore, the GCF (greatest common factor) = 900/180 = 5.
What are the Methods to Find LCM of 20 and 45?
The commonly used methods to find the LCM of 20 and 45 are:
 Prime Factorization Method
 Division Method
 Listing Multiples
What is the Least Perfect Square Divisible by 20 and 45?
The least number divisible by 20 and 45 = LCM(20, 45)
LCM of 20 and 45 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 20 and 45 = LCM(20, 45) × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
How to Find the LCM of 20 and 45 by Prime Factorization?
To find the LCM of 20 and 45 using prime factorization, we will find the prime factors, (20 = 2 × 2 × 5) and (45 = 3 × 3 × 5). LCM of 20 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 20 and 45.
⇒ LCM of 20, 45 = 2^{2} × 3^{2} × 5^{1} = 180.
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