LCM of 25 and 80

LCM of 25 and 80 is the smallest number among all common multiples of 25 and 80. The first few multiples of 25 and 80 are (25, 50, 75, 100, 125, 150, 175, . . . ) and (80, 160, 240, 320, 400, 480, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 80 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 25 and 80 is 400.

Explanation:

The LCM of two non-zero integers, x(25) and y(80), is the smallest positive integer m(400) that is divisible by both x(25) and y(80) without any remainder.

The methods to find the LCM of 25 and 80 are explained below.

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

LCM of 25 and 80 by Prime Factorization

Prime factorization of 25 and 80 is (5 × 5) = 5² and (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹ respectively. LCM of 25 and 80 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 5² = 400.
Hence, the LCM of 25 and 80 by prime factorization is 400.

LCM of 25 and 80 by Division Method

To calculate the LCM of 25 and 80 by the division method, we will divide the numbers(25, 80) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 80.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 80. Write this prime number(2) on the left of the given numbers(25 and 80), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (25, 80) 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 80 is the product of all prime numbers on the left, i.e. LCM(25, 80) by division method = 2 × 2 × 2 × 2 × 5 × 5 = 400.

LCM of 25 and 80 by Listing Multiples

To calculate the LCM of 25 and 80 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, 175, . . . ) and 80 (80, 160, 240, 320, 400, 480, . . . . )
• Step 2: The common multiples from the multiples of 25 and 80 are 400, 800, . . .
• Step 3: The smallest common multiple of 25 and 80 is 400.

∴ The least common multiple of 25 and 80 = 400.

☛ Also Check:

• LCM of 18 and 45 - 90
• LCM of 49 and 63 - 441
• LCM of 3 and 4 - 12
• LCM of 4, 9 and 10 - 180
• LCM of 16 and 64 - 64
• LCM of 3, 4 and 6 - 12
• LCM of 10 and 15 - 30

FAQs on LCM of 25 and 80

What is the LCM of 25 and 80?

The LCM of 25 and 80 is 400. To find the least common multiple of 25 and 80, we need to find the multiples of 25 and 80 (multiples of 25 = 25, 50, 75, 100 . . . . 400; multiples of 80 = 80, 160, 240, 320 . . . . 400) and choose the smallest multiple that is exactly divisible by 25 and 80, i.e., 400.

What are the Methods to Find LCM of 25 and 80?

The commonly used methods to find the LCM of 25 and 80 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

How to Find the LCM of 25 and 80 by Prime Factorization?

To find the LCM of 25 and 80 using prime factorization, we will find the prime factors, (25 = 5 × 5) and (80 = 2 × 2 × 2 × 2 × 5). LCM of 25 and 80 is the product of prime factors raised to their respective highest exponent among the numbers 25 and 80.
⇒ LCM of 25, 80 = 2⁴ × 5² = 400.

What is the Least Perfect Square Divisible by 25 and 80?

The least number divisible by 25 and 80 = LCM(25, 80)
LCM of 25 and 80 = 2 × 2 × 2 × 2 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 25 and 80 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

If the LCM of 80 and 25 is 400, Find its GCF.

LCM(80, 25) × GCF(80, 25) = 80 × 25
Since the LCM of 80 and 25 = 400
⇒ 400 × GCF(80, 25) = 2000
Therefore, the greatest common factor = 2000/400 = 5.