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LCM of 38 and 25

LCM of 38 and 25 is the smallest number among all common multiples of 38 and 25. The first few multiples of 38 and 25 are (38, 76, 114, 152, 190, 228, 266, . . . ) and (25, 50, 75, 100, 125, 150, 175, . . . ) respectively. There are 3 commonly used methods to find LCM of 38 and 25 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 38 and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 38 and 25?

Answer: LCM of 38 and 25 is 950.

Explanation:

The LCM of two non-zero integers, x(38) and y(25), is the smallest positive integer m(950) that is divisible by both x(38) and y(25) without any remainder.

Methods to Find LCM of 38 and 25

The methods to find the LCM of 38 and 25 are explained below.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 38 and 25 by Division Method

To calculate the LCM of 38 and 25 by the division method, we will divide the numbers(38, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 38 and 25.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 38 and 25. Write this prime number(2) on the left of the given numbers(38 and 25), separated as per the ladder arrangement.
Step 2: If any of the given numbers (38, 25) 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 38 and 25 is the product of all prime numbers on the left, i.e. LCM(38, 25) by division method = 2 × 5 × 5 × 19 = 950.

LCM of 38 and 25 by Listing Multiples

To calculate the LCM of 38 and 25 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 38 (38, 76, 114, 152, 190, 228, 266, . . . ) and 25 (25, 50, 75, 100, 125, 150, 175, . . . . )
Step 2: The common multiples from the multiples of 38 and 25 are 950, 1900, . . .
Step 3: The smallest common multiple of 38 and 25 is 950.

∴ The least common multiple of 38 and 25 = 950.

LCM of 38 and 25 by Prime Factorization

Prime factorization of 38 and 25 is (2 × 19) = 2¹ × 19¹ and (5 × 5) = 5² respectively. LCM of 38 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5² × 19¹ = 950.
Hence, the LCM of 38 and 25 by prime factorization is 950.

☛ Also Check:

LCM of 38 and 25 Examples

Example 1: The product of two numbers is 950. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 950
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 950/1
Therefore, the LCM is 950.
The probable combination for the given case is LCM(38, 25) = 950.
Example 2: The GCD and LCM of two numbers are 1 and 950 respectively. If one number is 38, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 38 × b
⇒ b = (GCD × LCM)/38
⇒ b = (1 × 950)/38
⇒ b = 25
Therefore, the other number is 25.
Example 3: Verify the relationship between GCF and LCM of 38 and 25.

Solution:

The relation between GCF and LCM of 38 and 25 is given as,
LCM(38, 25) × GCF(38, 25) = Product of 38, 25
Prime factorization of 38 and 25 is given as, 38 = (2 × 19) = 2¹ × 19¹ and 25 = (5 × 5) = 5²
LCM(38, 25) = 950
GCF(38, 25) = 1
LHS = LCM(38, 25) × GCF(38, 25) = 950 × 1 = 950
RHS = Product of 38, 25 = 38 × 25 = 950
⇒ LHS = RHS = 950
Hence, verified.

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FAQs on LCM of 38 and 25

What is the LCM of 38 and 25?

The LCM of 38 and 25 is 950. To find the LCM (least common multiple) of 38 and 25, we need to find the multiples of 38 and 25 (multiples of 38 = 38, 76, 114, 152 . . . . 950; multiples of 25 = 25, 50, 75, 100 . . . . 950) and choose the smallest multiple that is exactly divisible by 38 and 25, i.e., 950.

Which of the following is the LCM of 38 and 25? 5, 950, 15, 20

The value of LCM of 38, 25 is the smallest common multiple of 38 and 25. The number satisfying the given condition is 950.

If the LCM of 25 and 38 is 950, Find its GCF.

LCM(25, 38) × GCF(25, 38) = 25 × 38
Since the LCM of 25 and 38 = 950
⇒ 950 × GCF(25, 38) = 950
Therefore, the GCF (greatest common factor) = 950/950 = 1.

What is the Relation Between GCF and LCM of 38, 25?

The following equation can be used to express the relation between GCF and LCM of 38 and 25, i.e. GCF × LCM = 38 × 25.

How to Find the LCM of 38 and 25 by Prime Factorization?

To find the LCM of 38 and 25 using prime factorization, we will find the prime factors, (38 = 2 × 19) and (25 = 5 × 5). LCM of 38 and 25 is the product of prime factors raised to their respective highest exponent among the numbers 38 and 25.
⇒ LCM of 38, 25 = 2¹ × 5² × 19¹ = 950.

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