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

LCM of 8, 9, and 25

LCM of 8, 9, and 25 is the smallest number among all common multiples of 8, 9, and 25. The first few multiples of 8, 9, and 25 are (8, 16, 24, 32, 40 . . .), (9, 18, 27, 36, 45 . . .), and (25, 50, 75, 100, 125 . . .) respectively. There are 3 commonly used methods to find LCM of 8, 9, 25 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 8, 9, and 25
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 8, 9, and 25?

Answer: LCM of 8, 9, and 25 is 1800.

Explanation:

The LCM of three non-zero integers, a(8), b(9), and c(25), is the smallest positive integer m(1800) that is divisible by a(8), b(9), and c(25) without any remainder.

Methods to Find LCM of 8, 9, and 25

The methods to find the LCM of 8, 9, and 25 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 8, 9, and 25 by Division Method

To calculate the LCM of 8, 9, and 25 by the division method, we will divide the numbers(8, 9, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 8, 9, and 25.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8, 9, and 25. Write this prime number(2) on the left of the given numbers(8, 9, and 25), separated as per the ladder arrangement.
Step 2: If any of the given numbers (8, 9, 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 8, 9, and 25 is the product of all prime numbers on the left, i.e. LCM(8, 9, 25) by division method = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800.

LCM of 8, 9, and 25 by Prime Factorization

Prime factorization of 8, 9, and 25 is (2 × 2 × 2) = 2³, (3 × 3) = 3², and (5 × 5) = 5² respectively. LCM of 8, 9, and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² × 5² = 1800.
Hence, the LCM of 8, 9, and 25 by prime factorization is 1800.

LCM of 8, 9, and 25 by Listing Multiples

To calculate the LCM of 8, 9, 25 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 8 (8, 16, 24, 32, 40 . . .), 9 (9, 18, 27, 36, 45 . . .), and 25 (25, 50, 75, 100, 125 . . .).
Step 2: The common multiples from the multiples of 8, 9, and 25 are 1800, 3600, . . .
Step 3: The smallest common multiple of 8, 9, and 25 is 1800.

∴ The least common multiple of 8, 9, and 25 = 1800.

☛ Also Check:

LCM of 8, 9, and 25 Examples

Example 1: Calculate the LCM of 8, 9, and 25 using the GCD of the given numbers.

Solution:

Prime factorization of 8, 9, 25:
- 8 = 2³
- 9 = 3²
- 25 = 5²
Therefore, GCD(8, 9) = 1, GCD(9, 25) = 1, GCD(8, 25) = 1, GCD(8, 9, 25) = 1
We know,
LCM(8, 9, 25) = [(8 × 9 × 25) × GCD(8, 9, 25)]/[GCD(8, 9) × GCD(9, 25) × GCD(8, 25)]
LCM(8, 9, 25) = (1800 × 1)/(1 × 1 × 1) = 1800
⇒LCM(8, 9, 25) = 1800
Example 2: Find the smallest number that is divisible by 8, 9, 25 exactly.

Solution:

The value of LCM(8, 9, 25) will be the smallest number that is exactly divisible by 8, 9, and 25.
⇒ Multiples of 8, 9, and 25:
- Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . . ., 1768, 1776, 1784, 1792, 1800, . . . .
- Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 1773, 1782, 1791, 1800, . . . .
- Multiples of 25 = 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, . . . ., 1750, 1775, 1800, . . . .
Therefore, the LCM of 8, 9, and 25 is 1800.
Example 3: Verify the relationship between the GCD and LCM of 8, 9, and 25.

Solution:

The relation between GCD and LCM of 8, 9, and 25 is given as,
LCM(8, 9, 25) = [(8 × 9 × 25) × GCD(8, 9, 25)]/[GCD(8, 9) × GCD(9, 25) × GCD(8, 25)]
⇒ Prime factorization of 8, 9 and 25:
- 8 = 2³
- 9 = 3²
- 25 = 5²
∴ GCD of (8, 9), (9, 25), (8, 25) and (8, 9, 25) = 1, 1, 1 and 1 respectively.
Now, LHS = LCM(8, 9, 25) = 1800.
And, RHS = [(8 × 9 × 25) × GCD(8, 9, 25)]/[GCD(8, 9) × GCD(9, 25) × GCD(8, 25)] = [(1800) × 1]/[1 × 1 × 1] = 1800
LHS = RHS = 1800.
Hence verified.

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 8, 9, and 25

What is the LCM of 8, 9, and 25?

The LCM of 8, 9, and 25 is 1800. To find the least common multiple (LCM) of 8, 9, and 25, we need to find the multiples of 8, 9, and 25 (multiples of 8 = 8, 16, 24, 32 . . . . 1800 . . . . ; multiples of 9 = 9, 18, 27, 36 . . . . 1800 . . . . ; multiples of 25 = 25, 50, 75, 100 . . . . 1800 . . . . ) and choose the smallest multiple that is exactly divisible by 8, 9, and 25, i.e., 1800.

How to Find the LCM of 8, 9, and 25 by Prime Factorization?

To find the LCM of 8, 9, and 25 using prime factorization, we will find the prime factors, (8 = 2³), (9 = 3²), and (25 = 5²). LCM of 8, 9, and 25 is the product of prime factors raised to their respective highest exponent among the numbers 8, 9, and 25.
⇒ LCM of 8, 9, 25 = 2³ × 3² × 5² = 1800.

What is the Relation Between GCF and LCM of 8, 9, 25?

The following equation can be used to express the relation between GCF and LCM of 8, 9, 25, i.e. LCM(8, 9, 25) = [(8 × 9 × 25) × GCF(8, 9, 25)]/[GCF(8, 9) × GCF(9, 25) × GCF(8, 25)].

What is the Least Perfect Square Divisible by 8, 9, and 25?

The least number divisible by 8, 9, and 25 = LCM(8, 9, 25)
LCM of 8, 9, and 25 = 2 × 2 × 2 × 3 × 3 × 5 × 5 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 8, 9, and 25 = LCM(8, 9, 25) × 2 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

Download FREE Study Materials

LCM and GCF

Math worksheets and
visual curriculum