LCM of 18 and 25

LCM of 18 and 25 is the smallest number among all common multiples of 18 and 25. The first few multiples of 18 and 25 are (18, 36, 54, 72, 90, . . . ) and (25, 50, 75, 100, 125, 150, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 25 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 18 and 25 is 450.

Explanation:

The LCM of two non-zero integers, x(18) and y(25), is the smallest positive integer m(450) that is divisible by both x(18) and y(25) without any remainder.

Let's look at the different methods for finding the LCM of 18 and 25.

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

LCM of 18 and 25 by Listing Multiples

To calculate the LCM of 18 and 25 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 18 (18, 36, 54, 72, 90, . . . ) and 25 (25, 50, 75, 100, 125, 150, . . . . )
• Step 2: The common multiples from the multiples of 18 and 25 are 450, 900, . . .
• Step 3: The smallest common multiple of 18 and 25 is 450.

∴ The least common multiple of 18 and 25 = 450.

LCM of 18 and 25 by Prime Factorization

Prime factorization of 18 and 25 is (2 × 3 × 3) = 2¹ × 3² and (5 × 5) = 5² respectively. LCM of 18 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5² = 450.
Hence, the LCM of 18 and 25 by prime factorization is 450.

LCM of 18 and 25 by Division Method

To calculate the LCM of 18 and 25 by the division method, we will divide the numbers(18, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 25.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 25. Write this prime number(2) on the left of the given numbers(18 and 25), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (18, 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 18 and 25 is the product of all prime numbers on the left, i.e. LCM(18, 25) by division method = 2 × 3 × 3 × 5 × 5 = 450.

☛ Also Check:

• LCM of 30 and 35 - 210
• LCM of 30, 40 and 60 - 120
• LCM of 4 and 15 - 60
• LCM of 3 and 12 - 12
• LCM of 3 and 21 - 21
• LCM of 50 and 60 - 300
• LCM of 3, 4 and 6 - 12

FAQs on LCM of 18 and 25

What is the LCM of 18 and 25?

The LCM of 18 and 25 is 450. To find the least common multiple (LCM) of 18 and 25, we need to find the multiples of 18 and 25 (multiples of 18 = 18, 36, 54, 72 . . . . 450; multiples of 25 = 25, 50, 75, 100 . . . . 450) and choose the smallest multiple that is exactly divisible by 18 and 25, i.e., 450.

What is the Relation Between GCF and LCM of 18, 25?

The following equation can be used to express the relation between GCF and LCM of 18 and 25, i.e. GCF × LCM = 18 × 25.

If the LCM of 25 and 18 is 450, Find its GCF.

LCM(25, 18) × GCF(25, 18) = 25 × 18
Since the LCM of 25 and 18 = 450
⇒ 450 × GCF(25, 18) = 450
Therefore, the GCF (greatest common factor) = 450/450 = 1.

What is the Least Perfect Square Divisible by 18 and 25?

The least number divisible by 18 and 25 = LCM(18, 25)
LCM of 18 and 25 = 2 × 3 × 3 × 5 × 5 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 18 and 25 = LCM(18, 25) × 2 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

How to Find the LCM of 18 and 25 by Prime Factorization?

To find the LCM of 18 and 25 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (25 = 5 × 5). LCM of 18 and 25 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 25.
⇒ LCM of 18, 25 = 2¹ × 3² × 5² = 450.