LCM of 12 and 20
LCM of 12 and 20 is the smallest number among all common multiples of 12 and 20. The first few multiples of 12 and 20 are (12, 24, 36, 48, 60, 72, . . . ) and (20, 40, 60, 80, 100, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 20  by listing multiples, by prime factorization, and by division method.
1.  LCM of 12 and 20 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 12 and 20?
Answer: LCM of 12 and 20 is 60.
Explanation:
The LCM of two nonzero integers, x(12) and y(20), is the smallest positive integer m(60) that is divisible by both x(12) and y(20) without any remainder.
Methods to Find LCM of 12 and 20
Let's look at the different methods for finding the LCM of 12 and 20.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 12 and 20 by Prime Factorization
Prime factorization of 12 and 20 is (2 × 2 × 3) = 2^{2} × 3^{1} and (2 × 2 × 5) = 2^{2} × 5^{1} respectively. LCM of 12 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{1} × 5^{1} = 60.
Hence, the LCM of 12 and 20 by prime factorization is 60.
LCM of 12 and 20 by Division Method
To calculate the LCM of 12 and 20 by the division method, we will divide the numbers(12, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 20.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 20. Write this prime number(2) on the left of the given numbers(12 and 20), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (12, 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 12 and 20 is the product of all prime numbers on the left, i.e. LCM(12, 20) by division method = 2 × 2 × 3 × 5 = 60.
LCM of 12 and 20 by Listing Multiples
To calculate the LCM of 12 and 20 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and 20 (20, 40, 60, 80, 100, 120, . . . . )
 Step 2: The common multiples from the multiples of 12 and 20 are 60, 120, . . .
 Step 3: The smallest common multiple of 12 and 20 is 60.
∴ The least common multiple of 12 and 20 = 60.
☛ Also Check:
 LCM of 14 and 42  42
 LCM of 14 and 35  70
 LCM of 14 and 28  28
 LCM of 14 and 24  168
 LCM of 14 and 22  154
 LCM of 14 and 21  42
 LCM of 14 and 20  140
LCM of 12 and 20 Examples

Example 1: The product of two numbers is 240. If their GCD is 4, what is their LCM?
Solution:
Given: GCD = 4
product of numbers = 240
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 240/4
Therefore, the LCM is 60.
The probable combination for the given case is LCM(12, 20) = 60. 
Example 2: Find the smallest number that is divisible by 12 and 20 exactly.
Solution:
The smallest number that is divisible by 12 and 20 exactly is their LCM.
⇒ Multiples of 12 and 20: Multiples of 12 = 12, 24, 36, 48, 60, . . . .
 Multiples of 20 = 20, 40, 60, 80, 100, . . . .
Therefore, the LCM of 12 and 20 is 60.

Example 3: The GCD and LCM of two numbers are 4 and 60 respectively. If one number is 12, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 12 × z
⇒ z = (GCD × LCM)/12
⇒ z = (4 × 60)/12
⇒ z = 20
Therefore, the other number is 20.
FAQs on LCM of 12 and 20
What is the LCM of 12 and 20?
The LCM of 12 and 20 is 60. To find the least common multiple of 12 and 20, we need to find the multiples of 12 and 20 (multiples of 12 = 12, 24, 36, 48 . . . . 60; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 12 and 20, i.e., 60.
What are the Methods to Find LCM of 12 and 20?
The commonly used methods to find the LCM of 12 and 20 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
If the LCM of 20 and 12 is 60, Find its GCF.
LCM(20, 12) × GCF(20, 12) = 20 × 12
Since the LCM of 20 and 12 = 60
⇒ 60 × GCF(20, 12) = 240
Therefore, the GCF (greatest common factor) = 240/60 = 4.
What is the Relation Between GCF and LCM of 12, 20?
The following equation can be used to express the relation between GCF and LCM of 12 and 20, i.e. GCF × LCM = 12 × 20.
Which of the following is the LCM of 12 and 20? 60, 16, 2, 45
The value of LCM of 12, 20 is the smallest common multiple of 12 and 20. The number satisfying the given condition is 60.
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