LCM of 25 and 4

LCM of 25 and 4 is the smallest number among all common multiples of 25 and 4. The first few multiples of 25 and 4 are (25, 50, 75, 100, 125, 150, . . . ) and (4, 8, 12, 16, 20, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 4 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 25 and 4 is 100.

Explanation:

The LCM of two non-zero integers, x(25) and y(4), is the smallest positive integer m(100) that is divisible by both x(25) and y(4) without any remainder.

The methods to find the LCM of 25 and 4 are explained below.

• By Prime Factorization Method
• By Listing Multiples
• By Division Method

LCM of 25 and 4 by Prime Factorization

Prime factorization of 25 and 4 is (5 × 5) = 5² and (2 × 2) = 2² respectively. LCM of 25 and 4 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5² = 100.
Hence, the LCM of 25 and 4 by prime factorization is 100.

LCM of 25 and 4 by Listing Multiples

To calculate the LCM of 25 and 4 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 25 (25, 50, 75, 100, 125, 150, . . . ) and 4 (4, 8, 12, 16, 20, . . . . )
• Step 2: The common multiples from the multiples of 25 and 4 are 100, 200, . . .
• Step 3: The smallest common multiple of 25 and 4 is 100.

∴ The least common multiple of 25 and 4 = 100.

LCM of 25 and 4 by Division Method

To calculate the LCM of 25 and 4 by the division method, we will divide the numbers(25, 4) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 4.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 4. Write this prime number(2) on the left of the given numbers(25 and 4), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (25, 4) 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 25 and 4 is the product of all prime numbers on the left, i.e. LCM(25, 4) by division method = 2 × 2 × 5 × 5 = 100.

☛ Also Check:

• LCM of 7 and 9 - 63
• LCM of 6 and 30 - 30
• LCM of 45 and 72 - 360
• LCM of 36 and 90 - 180
• LCM of 84 and 90 - 1260
• LCM of 24 and 40 - 120
• LCM of 15, 20 and 25 - 300

FAQs on LCM of 25 and 4

What is the LCM of 25 and 4?

The LCM of 25 and 4 is 100. To find the least common multiple of 25 and 4, we need to find the multiples of 25 and 4 (multiples of 25 = 25, 50, 75, 100; multiples of 4 = 4, 8, 12, 16 . . . . 100) and choose the smallest multiple that is exactly divisible by 25 and 4, i.e., 100.

If the LCM of 4 and 25 is 100, Find its GCF.

LCM(4, 25) × GCF(4, 25) = 4 × 25
Since the LCM of 4 and 25 = 100
⇒ 100 × GCF(4, 25) = 100
Therefore, the GCF (greatest common factor) = 100/100 = 1.

How to Find the LCM of 25 and 4 by Prime Factorization?

To find the LCM of 25 and 4 using prime factorization, we will find the prime factors, (25 = 5 × 5) and (4 = 2 × 2). LCM of 25 and 4 is the product of prime factors raised to their respective highest exponent among the numbers 25 and 4.
⇒ LCM of 25, 4 = 2² × 5² = 100.

Which of the following is the LCM of 25 and 4? 27, 24, 50, 100

The value of LCM of 25, 4 is the smallest common multiple of 25 and 4. The number satisfying the given condition is 100.

What are the Methods to Find LCM of 25 and 4?

The commonly used methods to find the LCM of 25 and 4 are:

• Prime Factorization Method
• Listing Multiples
• Division Method