LCM of 100 and 200
LCM of 100 and 200 is the smallest number among all common multiples of 100 and 200. The first few multiples of 100 and 200 are (100, 200, 300, 400, 500, 600, 700, . . . ) and (200, 400, 600, 800, . . . ) respectively. There are 3 commonly used methods to find LCM of 100 and 200  by prime factorization, by division method, and by listing multiples.
1.  LCM of 100 and 200 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 100 and 200?
Answer: LCM of 100 and 200 is 200.
Explanation:
The LCM of two nonzero integers, x(100) and y(200), is the smallest positive integer m(200) that is divisible by both x(100) and y(200) without any remainder.
Methods to Find LCM of 100 and 200
Let's look at the different methods for finding the LCM of 100 and 200.
 By Division Method
 By Listing Multiples
 By Prime Factorization Method
LCM of 100 and 200 by Division Method
To calculate the LCM of 100 and 200 by the division method, we will divide the numbers(100, 200) by their prime factors (preferably common). The product of these divisors gives the LCM of 100 and 200.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 100 and 200. Write this prime number(2) on the left of the given numbers(100 and 200), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (100, 200) 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 100 and 200 is the product of all prime numbers on the left, i.e. LCM(100, 200) by division method = 2 × 2 × 2 × 5 × 5 = 200.
LCM of 100 and 200 by Listing Multiples
To calculate the LCM of 100 and 200 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 100 (100, 200, 300, 400, 500, 600, 700, . . . ) and 200 (200, 400, 600, 800, . . . . )
 Step 2: The common multiples from the multiples of 100 and 200 are 200, 400, . . .
 Step 3: The smallest common multiple of 100 and 200 is 200.
∴ The least common multiple of 100 and 200 = 200.
LCM of 100 and 200 by Prime Factorization
Prime factorization of 100 and 200 is (2 × 2 × 5 × 5) = 2^{2} × 5^{2} and (2 × 2 × 2 × 5 × 5) = 2^{3} × 5^{2} respectively. LCM of 100 and 200 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 5^{2} = 200.
Hence, the LCM of 100 and 200 by prime factorization is 200.
☛ Also Check:
 LCM of 4 and 12  12
 LCM of 4 and 10  20
 LCM of 39 and 65  195
 LCM of 37 and 49  1813
 LCM of 36 and 90  180
 LCM of 36 and 84  252
 LCM of 36 and 81  324
LCM of 100 and 200 Examples

Example 1: Verify the relationship between GCF and LCM of 100 and 200.
Solution:
The relation between GCF and LCM of 100 and 200 is given as,
LCM(100, 200) × GCF(100, 200) = Product of 100, 200
Prime factorization of 100 and 200 is given as, 100 = (2 × 2 × 5 × 5) = 2^{2} × 5^{2} and 200 = (2 × 2 × 2 × 5 × 5) = 2^{3} × 5^{2}
LCM(100, 200) = 200
GCF(100, 200) = 100
LHS = LCM(100, 200) × GCF(100, 200) = 200 × 100 = 20000
RHS = Product of 100, 200 = 100 × 200 = 20000
⇒ LHS = RHS = 20000
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 100 and 200 respectively. If one number is 200, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 200 × y
⇒ y = (GCD × LCM)/200
⇒ y = (100 × 200)/200
⇒ y = 100
Therefore, the other number is 100. 
Example 3: Find the smallest number that is divisible by 100 and 200 exactly.
Solution:
The smallest number that is divisible by 100 and 200 exactly is their LCM.
⇒ Multiples of 100 and 200: Multiples of 100 = 100, 200, 300, 400, 500, 600, 700, . . . .
 Multiples of 200 = 200, 400, 600, 800, 1000, 1200, 1400, . . . .
Therefore, the LCM of 100 and 200 is 200.
FAQs on LCM of 100 and 200
What is the LCM of 100 and 200?
The LCM of 100 and 200 is 200. To find the least common multiple (LCM) of 100 and 200, we need to find the multiples of 100 and 200 (multiples of 100 = 100, 200, 300, 400; multiples of 200 = 200, 400, 600, 800) and choose the smallest multiple that is exactly divisible by 100 and 200, i.e., 200.
What are the Methods to Find LCM of 100 and 200?
The commonly used methods to find the LCM of 100 and 200 are:
 Prime Factorization Method
 Division Method
 Listing Multiples
What is the Relation Between GCF and LCM of 100, 200?
The following equation can be used to express the relation between GCF and LCM of 100 and 200, i.e. GCF × LCM = 100 × 200.
If the LCM of 200 and 100 is 200, Find its GCF.
LCM(200, 100) × GCF(200, 100) = 200 × 100
Since the LCM of 200 and 100 = 200
⇒ 200 × GCF(200, 100) = 20000
Therefore, the greatest common factor (GCF) = 20000/200 = 100.
How to Find the LCM of 100 and 200 by Prime Factorization?
To find the LCM of 100 and 200 using prime factorization, we will find the prime factors, (100 = 2 × 2 × 5 × 5) and (200 = 2 × 2 × 2 × 5 × 5). LCM of 100 and 200 is the product of prime factors raised to their respective highest exponent among the numbers 100 and 200.
⇒ LCM of 100, 200 = 2^{3} × 5^{2} = 200.
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