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LCM of 100 and 190

LCM of 100 and 190 is the smallest number among all common multiples of 100 and 190. The first few multiples of 100 and 190 are (100, 200, 300, 400, 500, . . . ) and (190, 380, 570, 760, 950, 1140, . . . ) respectively. There are 3 commonly used methods to find LCM of 100 and 190 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 100 and 190
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 100 and 190?

Answer: LCM of 100 and 190 is 1900.

Explanation:

The LCM of two non-zero integers, x(100) and y(190), is the smallest positive integer m(1900) that is divisible by both x(100) and y(190) without any remainder.

Methods to Find LCM of 100 and 190

Let's look at the different methods for finding the LCM of 100 and 190.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 100 and 190 by Prime Factorization

Prime factorization of 100 and 190 is (2 × 2 × 5 × 5) = 2² × 5² and (2 × 5 × 19) = 2¹ × 5¹ × 19¹ respectively. LCM of 100 and 190 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5² × 19¹ = 1900.
Hence, the LCM of 100 and 190 by prime factorization is 1900.

LCM of 100 and 190 by Listing Multiples

To calculate the LCM of 100 and 190 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, . . . ) and 190 (190, 380, 570, 760, 950, 1140, . . . . )
Step 2: The common multiples from the multiples of 100 and 190 are 1900, 3800, . . .
Step 3: The smallest common multiple of 100 and 190 is 1900.

∴ The least common multiple of 100 and 190 = 1900.

LCM of 100 and 190 by Division Method

To calculate the LCM of 100 and 190 by the division method, we will divide the numbers(100, 190) by their prime factors (preferably common). The product of these divisors gives the LCM of 100 and 190.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 100 and 190. Write this prime number(2) on the left of the given numbers(100 and 190), separated as per the ladder arrangement.
Step 2: If any of the given numbers (100, 190) 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 190 is the product of all prime numbers on the left, i.e. LCM(100, 190) by division method = 2 × 2 × 5 × 5 × 19 = 1900.

☛ Also Check:

LCM of 100 and 190 Examples

Example 1: Find the smallest number that is divisible by 100 and 190 exactly.

Solution:

The value of LCM(100, 190) will be the smallest number that is exactly divisible by 100 and 190.
⇒ Multiples of 100 and 190:
- Multiples of 100 = 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, . . . ., 1700, 1800, 1900, . . . .
- Multiples of 190 = 190, 380, 570, 760, 950, 1140, 1330, 1520, 1710, 1900, . . . ., 1520, 1710, 1900, . . . .
Therefore, the LCM of 100 and 190 is 1900.
Example 2: The GCD and LCM of two numbers are 10 and 1900 respectively. If one number is 100, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 100 × z
⇒ z = (GCD × LCM)/100
⇒ z = (10 × 1900)/100
⇒ z = 190
Therefore, the other number is 190.
Example 3: Verify the relationship between GCF and LCM of 100 and 190.

Solution:

The relation between GCF and LCM of 100 and 190 is given as,
LCM(100, 190) × GCF(100, 190) = Product of 100, 190
Prime factorization of 100 and 190 is given as, 100 = (2 × 2 × 5 × 5) = 2² × 5² and 190 = (2 × 5 × 19) = 2¹ × 5¹ × 19¹
LCM(100, 190) = 1900
GCF(100, 190) = 10
LHS = LCM(100, 190) × GCF(100, 190) = 1900 × 10 = 19000
RHS = Product of 100, 190 = 100 × 190 = 19000
⇒ LHS = RHS = 19000
Hence, verified.

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FAQs on LCM of 100 and 190

What is the LCM of 100 and 190?

The LCM of 100 and 190 is 1900. To find the LCM (least common multiple) of 100 and 190, we need to find the multiples of 100 and 190 (multiples of 100 = 100, 200, 300, 400 . . . . 1900; multiples of 190 = 190, 380, 570, 760 . . . . 1900) and choose the smallest multiple that is exactly divisible by 100 and 190, i.e., 1900.

What is the Least Perfect Square Divisible by 100 and 190?

The least number divisible by 100 and 190 = LCM(100, 190)
LCM of 100 and 190 = 2 × 2 × 5 × 5 × 19 [Incomplete pair(s): 19]
⇒ Least perfect square divisible by each 100 and 190 = LCM(100, 190) × 19 = 36100 [Square root of 36100 = √36100 = ±190]
Therefore, 36100 is the required number.

If the LCM of 190 and 100 is 1900, Find its GCF.

LCM(190, 100) × GCF(190, 100) = 190 × 100
Since the LCM of 190 and 100 = 1900
⇒ 1900 × GCF(190, 100) = 19000
Therefore, the greatest common factor (GCF) = 19000/1900 = 10.

Which of the following is the LCM of 100 and 190? 27, 11, 16, 1900

The value of LCM of 100, 190 is the smallest common multiple of 100 and 190. The number satisfying the given condition is 1900.

How to Find the LCM of 100 and 190 by Prime Factorization?

To find the LCM of 100 and 190 using prime factorization, we will find the prime factors, (100 = 2 × 2 × 5 × 5) and (190 = 2 × 5 × 19). LCM of 100 and 190 is the product of prime factors raised to their respective highest exponent among the numbers 100 and 190.
⇒ LCM of 100, 190 = 2² × 5² × 19¹ = 1900.

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