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LCM of 200 and 300

LCM of 200 and 300 is the smallest number among all common multiples of 200 and 300. The first few multiples of 200 and 300 are (200, 400, 600, 800, 1000, 1200, 1400, . . . ) and (300, 600, 900, 1200, 1500, . . . ) respectively. There are 3 commonly used methods to find LCM of 200 and 300 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 200 and 300
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 200 and 300?

Answer: LCM of 200 and 300 is 600.

Explanation:

The LCM of two non-zero integers, x(200) and y(300), is the smallest positive integer m(600) that is divisible by both x(200) and y(300) without any remainder.

Methods to Find LCM of 200 and 300

The methods to find the LCM of 200 and 300 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 200 and 300 by Division Method

To calculate the LCM of 200 and 300 by the division method, we will divide the numbers(200, 300) by their prime factors (preferably common). The product of these divisors gives the LCM of 200 and 300.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 200 and 300. Write this prime number(2) on the left of the given numbers(200 and 300), separated as per the ladder arrangement.
Step 2: If any of the given numbers (200, 300) 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 200 and 300 is the product of all prime numbers on the left, i.e. LCM(200, 300) by division method = 2 × 2 × 2 × 3 × 5 × 5 = 600.

LCM of 200 and 300 by Prime Factorization

Prime factorization of 200 and 300 is (2 × 2 × 2 × 5 × 5) = 2³ × 5² and (2 × 2 × 3 × 5 × 5) = 2² × 3¹ × 5² respectively. LCM of 200 and 300 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5² = 600.
Hence, the LCM of 200 and 300 by prime factorization is 600.

LCM of 200 and 300 by Listing Multiples

To calculate the LCM of 200 and 300 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 200 (200, 400, 600, 800, 1000, 1200, 1400, . . . ) and 300 (300, 600, 900, 1200, 1500, . . . . )
Step 2: The common multiples from the multiples of 200 and 300 are 600, 1200, . . .
Step 3: The smallest common multiple of 200 and 300 is 600.

∴ The least common multiple of 200 and 300 = 600.

☛ Also Check:

LCM of 200 and 300 Examples

Example 1: Verify the relationship between GCF and LCM of 200 and 300.

Solution:

The relation between GCF and LCM of 200 and 300 is given as,
LCM(200, 300) × GCF(200, 300) = Product of 200, 300
Prime factorization of 200 and 300 is given as, 200 = (2 × 2 × 2 × 5 × 5) = 2³ × 5² and 300 = (2 × 2 × 3 × 5 × 5) = 2² × 3¹ × 5²
LCM(200, 300) = 600
GCF(200, 300) = 100
LHS = LCM(200, 300) × GCF(200, 300) = 600 × 100 = 60000
RHS = Product of 200, 300 = 200 × 300 = 60000
⇒ LHS = RHS = 60000
Hence, verified.
Example 2: Find the smallest number that is divisible by 200 and 300 exactly.

Solution:

The smallest number that is divisible by 200 and 300 exactly is their LCM.
⇒ Multiples of 200 and 300:
- Multiples of 200 = 200, 400, 600, 800, 1000, 1200, . . . .
- Multiples of 300 = 300, 600, 900, 1200, 1500, 1800, . . . .
Therefore, the LCM of 200 and 300 is 600.
Example 3: The product of two numbers is 60000. If their GCD is 100, what is their LCM?

Solution:

Given: GCD = 100
product of numbers = 60000
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 60000/100
Therefore, the LCM is 600.
The probable combination for the given case is LCM(200, 300) = 600.

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FAQs on LCM of 200 and 300

What is the LCM of 200 and 300?

The LCM of 200 and 300 is 600. To find the least common multiple (LCM) of 200 and 300, we need to find the multiples of 200 and 300 (multiples of 200 = 200, 400, 600, 800; multiples of 300 = 300, 600, 900, 1200) and choose the smallest multiple that is exactly divisible by 200 and 300, i.e., 600.

What is the Relation Between GCF and LCM of 200, 300?

The following equation can be used to express the relation between GCF and LCM of 200 and 300, i.e. GCF × LCM = 200 × 300.

What is the Least Perfect Square Divisible by 200 and 300?

The least number divisible by 200 and 300 = LCM(200, 300)
LCM of 200 and 300 = 2 × 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 200 and 300 = LCM(200, 300) × 2 × 3 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

Which of the following is the LCM of 200 and 300? 3, 5, 600, 24

The value of LCM of 200, 300 is the smallest common multiple of 200 and 300. The number satisfying the given condition is 600.

If the LCM of 300 and 200 is 600, Find its GCF.

LCM(300, 200) × GCF(300, 200) = 300 × 200
Since the LCM of 300 and 200 = 600
⇒ 600 × GCF(300, 200) = 60000
Therefore, the greatest common factor (GCF) = 60000/600 = 100.

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