A day full of math games & activities. Find one near you.

LCM of 25, 40, and 60

LCM of 25, 40, and 60 is the smallest number among all common multiples of 25, 40, and 60. The first few multiples of 25, 40, and 60 are (25, 50, 75, 100, 125 . . .), (40, 80, 120, 160, 200 . . .), and (60, 120, 180, 240, 300 . . .) respectively. There are 3 commonly used methods to find LCM of 25, 40, 60 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 25, 40, and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 25, 40, and 60?

Answer: LCM of 25, 40, and 60 is 600.

Explanation:

The LCM of three non-zero integers, a(25), b(40), and c(60), is the smallest positive integer m(600) that is divisible by a(25), b(40), and c(60) without any remainder.

Methods to Find LCM of 25, 40, and 60

Let's look at the different methods for finding the LCM of 25, 40, and 60.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 25, 40, and 60 by Prime Factorization

Prime factorization of 25, 40, and 60 is (5 × 5) = 5², (2 × 2 × 2 × 5) = 2³ × 5¹, and (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ respectively. LCM of 25, 40, and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5² = 600.
Hence, the LCM of 25, 40, and 60 by prime factorization is 600.

LCM of 25, 40, and 60 by Division Method

To calculate the LCM of 25, 40, and 60 by the division method, we will divide the numbers(25, 40, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 25, 40, and 60.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 25, 40, and 60. Write this prime number(2) on the left of the given numbers(25, 40, and 60), separated as per the ladder arrangement.
Step 2: If any of the given numbers (25, 40, 60) 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, 40, and 60 is the product of all prime numbers on the left, i.e. LCM(25, 40, 60) by division method = 2 × 2 × 2 × 3 × 5 × 5 = 600.

LCM of 25, 40, and 60 by Listing Multiples

To calculate the LCM of 25, 40, 60 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 . . .), 40 (40, 80, 120, 160, 200 . . .), and 60 (60, 120, 180, 240, 300 . . .).
Step 2: The common multiples from the multiples of 25, 40, and 60 are 600, 1200, . . .
Step 3: The smallest common multiple of 25, 40, and 60 is 600.

∴ The least common multiple of 25, 40, and 60 = 600.

☛ Also Check:

LCM of 25, 40, and 60 Examples

Example 1: Verify the relationship between the GCD and LCM of 25, 40, and 60.

Solution:

The relation between GCD and LCM of 25, 40, and 60 is given as,
LCM(25, 40, 60) = [(25 × 40 × 60) × GCD(25, 40, 60)]/[GCD(25, 40) × GCD(40, 60) × GCD(25, 60)]
⇒ Prime factorization of 25, 40 and 60:
- 25 = 5²
- 40 = 2³ × 5¹
- 60 = 2² × 3¹ × 5¹
∴ GCD of (25, 40), (40, 60), (25, 60) and (25, 40, 60) = 5, 20, 5 and 5 respectively.
Now, LHS = LCM(25, 40, 60) = 600.
And, RHS = [(25 × 40 × 60) × GCD(25, 40, 60)]/[GCD(25, 40) × GCD(40, 60) × GCD(25, 60)] = [(60000) × 5]/[5 × 20 × 5] = 600
LHS = RHS = 600.
Hence verified.
Example 2: Calculate the LCM of 25, 40, and 60 using the GCD of the given numbers.

Solution:

Prime factorization of 25, 40, 60:
- 25 = 5²
- 40 = 2³ × 5¹
- 60 = 2² × 3¹ × 5¹
Therefore, GCD(25, 40) = 5, GCD(40, 60) = 20, GCD(25, 60) = 5, GCD(25, 40, 60) = 5
We know,
LCM(25, 40, 60) = [(25 × 40 × 60) × GCD(25, 40, 60)]/[GCD(25, 40) × GCD(40, 60) × GCD(25, 60)]
LCM(25, 40, 60) = (60000 × 5)/(5 × 20 × 5) = 600
⇒LCM(25, 40, 60) = 600
Example 3: Find the smallest number that is divisible by 25, 40, 60 exactly.

Solution:

The value of LCM(25, 40, 60) will be the smallest number that is exactly divisible by 25, 40, and 60.
⇒ Multiples of 25, 40, and 60:
- Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 525, 550, 575, 600, . . . .
- Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 520, 560, 600, . . . .
- Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, . . . ., 480, 540, 600, . . . .
Therefore, the LCM of 25, 40, and 60 is 600.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on LCM of 25, 40, and 60

What is the LCM of 25, 40, and 60?

The LCM of 25, 40, and 60 is 600. To find the LCM of 25, 40, and 60, we need to find the multiples of 25, 40, and 60 (multiples of 25 = 25, 50, 75, 100 . . . . 600 . . . . ; multiples of 40 = 40, 80, 120, 160 . . . . 600 . . . . ; multiples of 60 = 60, 120, 180, 240 . . . . 600 . . . . ) and choose the smallest multiple that is exactly divisible by 25, 40, and 60, i.e., 600.

What is the Least Perfect Square Divisible by 25, 40, and 60?

The least number divisible by 25, 40, and 60 = LCM(25, 40, 60)
LCM of 25, 40, and 60 = 2 × 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 25, 40, and 60 = LCM(25, 40, 60) × 2 × 3 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

Which of the following is the LCM of 25, 40, and 60? 25, 50, 105, 600

The value of LCM of 25, 40, 60 is the smallest common multiple of 25, 40, and 60. The number satisfying the given condition is 600.

How to Find the LCM of 25, 40, and 60 by Prime Factorization?

To find the LCM of 25, 40, and 60 using prime factorization, we will find the prime factors, (25 = 5²), (40 = 2³ × 5¹), and (60 = 2² × 3¹ × 5¹). LCM of 25, 40, and 60 is the product of prime factors raised to their respective highest exponent among the numbers 25, 40, and 60.
⇒ LCM of 25, 40, 60 = 2³ × 3¹ × 5² = 600.

Download FREE Study Materials

LCM and GCF

Math worksheets and
visual curriculum