LCM of 25 and 40

LCM of 25 and 40 is the smallest number among all common multiples of 25 and 40. The first few multiples of 25 and 40 are (25, 50, 75, 100, 125, 150, 175, . . . ) and (40, 80, 120, 160, . . . ) respectively. There are 3 commonly used methods to find LCM of 25 and 40 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 25 and 40 is 200.

Explanation:

The LCM of two non-zero integers, x(25) and y(40), is the smallest positive integer m(200) that is divisible by both x(25) and y(40) without any remainder.

The methods to find the LCM of 25 and 40 are explained below.

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

LCM of 25 and 40 by Division Method

To calculate the LCM of 25 and 40 by the division method, we will divide the numbers(25, 40) by their prime factors (preferably common). The product of these divisors gives the LCM of 25 and 40.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25 and 40. Write this prime number(2) on the left of the given numbers(25 and 40), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (25, 40) 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 40 is the product of all prime numbers on the left, i.e. LCM(25, 40) by division method = 2 × 2 × 2 × 5 × 5 = 200.

LCM of 25 and 40 by Prime Factorization

Prime factorization of 25 and 40 is (5 × 5) = 5² and (2 × 2 × 2 × 5) = 2³ × 5¹ respectively. LCM of 25 and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5² = 200.
Hence, the LCM of 25 and 40 by prime factorization is 200.

LCM of 25 and 40 by Listing Multiples

To calculate the LCM of 25 and 40 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 40 (40, 80, 120, 160, . . . . )
• Step 2: The common multiples from the multiples of 25 and 40 are 200, 400, . . .
• Step 3: The smallest common multiple of 25 and 40 is 200.

∴ The least common multiple of 25 and 40 = 200.

☛ Also Check:

• LCM of 6 and 14 - 42
• LCM of 21 and 22 - 462
• LCM of 64 and 96 - 192
• LCM of 12 and 15 - 60
• LCM of 6 and 18 - 18
• LCM of 60 and 66 - 660
• LCM of 24, 36 and 72 - 72

FAQs on LCM of 25 and 40

What is the LCM of 25 and 40?

The LCM of 25 and 40 is 200. To find the least common multiple of 25 and 40, we need to find the multiples of 25 and 40 (multiples of 25 = 25, 50, 75, 100 . . . . 200; multiples of 40 = 40, 80, 120, 160 . . . . 200) and choose the smallest multiple that is exactly divisible by 25 and 40, i.e., 200.

What are the Methods to Find LCM of 25 and 40?

The commonly used methods to find the LCM of 25 and 40 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

Which of the following is the LCM of 25 and 40? 200, 16, 50, 40

The value of LCM of 25, 40 is the smallest common multiple of 25 and 40. The number satisfying the given condition is 200.

How to Find the LCM of 25 and 40 by Prime Factorization?

To find the LCM of 25 and 40 using prime factorization, we will find the prime factors, (25 = 5 × 5) and (40 = 2 × 2 × 2 × 5). LCM of 25 and 40 is the product of prime factors raised to their respective highest exponent among the numbers 25 and 40.
⇒ LCM of 25, 40 = 2³ × 5² = 200.

If the LCM of 40 and 25 is 200, Find its GCF.

LCM(40, 25) × GCF(40, 25) = 40 × 25
Since the LCM of 40 and 25 = 200
⇒ 200 × GCF(40, 25) = 1000
Therefore, the GCF (greatest common factor) = 1000/200 = 5.