LCM of 20 and 25

LCM of 20 and 25 is the smallest number among all common multiples of 20 and 25. The first few multiples of 20 and 25 are (20, 40, 60, 80, 100, 120, 140, . . . ) and (25, 50, 75, 100, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 25 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 20 and 25 is 100.

Explanation:

The LCM of two non-zero integers, x(20) and y(25), is the smallest positive integer m(100) that is divisible by both x(20) and y(25) without any remainder.

The methods to find the LCM of 20 and 25 are explained below.

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

LCM of 20 and 25 by Prime Factorization

Prime factorization of 20 and 25 is (2 × 2 × 5) = 2² × 5¹ and (5 × 5) = 5² respectively. LCM of 20 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5² = 100.
Hence, the LCM of 20 and 25 by prime factorization is 100.

LCM of 20 and 25 by Listing Multiples

To calculate the LCM of 20 and 25 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 20 (20, 40, 60, 80, 100, 120, 140, . . . ) and 25 (25, 50, 75, 100, . . . . )
• Step 2: The common multiples from the multiples of 20 and 25 are 100, 200, . . .
• Step 3: The smallest common multiple of 20 and 25 is 100.

∴ The least common multiple of 20 and 25 = 100.

LCM of 20 and 25 by Division Method

To calculate the LCM of 20 and 25 by the division method, we will divide the numbers(20, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 25.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 25. Write this prime number(2) on the left of the given numbers(20 and 25), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (20, 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 20 and 25 is the product of all prime numbers on the left, i.e. LCM(20, 25) by division method = 2 × 2 × 5 × 5 = 100.

☛ Also Check:

• LCM of 8 and 10 - 40
• LCM of 4, 9 and 10 - 180
• LCM of 17 and 34 - 34
• LCM of 3, 4 and 7 - 84
• LCM of 9 and 36 - 36
• LCM of 25 and 16 - 400
• LCM of 25 and 50 - 50

FAQs on LCM of 20 and 25

What is the LCM of 20 and 25?

The LCM of 20 and 25 is 100. To find the LCM (least common multiple) of 20 and 25, we need to find the multiples of 20 and 25 (multiples of 20 = 20, 40, 60, 80 . . . . 100; multiples of 25 = 25, 50, 75, 100) and choose the smallest multiple that is exactly divisible by 20 and 25, i.e., 100.

What are the Methods to Find LCM of 20 and 25?

The commonly used methods to find the LCM of 20 and 25 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Least Perfect Square Divisible by 20 and 25?

The least number divisible by 20 and 25 = LCM(20, 25)
LCM of 20 and 25 = 2 × 2 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 20 and 25 = 100 [Square root of 100 = √100 = ±10]
Therefore, 100 is the required number.

Which of the following is the LCM of 20 and 25? 24, 50, 16, 100

The value of LCM of 20, 25 is the smallest common multiple of 20 and 25. The number satisfying the given condition is 100.

If the LCM of 25 and 20 is 100, Find its GCF.

LCM(25, 20) × GCF(25, 20) = 25 × 20
Since the LCM of 25 and 20 = 100
⇒ 100 × GCF(25, 20) = 500
Therefore, the GCF = 500/100 = 5.