LCM of 15, 20, and 25

LCM of 15, 20, and 25 is the smallest number among all common multiples of 15, 20, and 25. The first few multiples of 15, 20, and 25 are (15, 30, 45, 60, 75 . . .), (20, 40, 60, 80, 100 . . .), and (25, 50, 75, 100, 125 . . .) respectively. There are 3 commonly used methods to find LCM of 15, 20, 25 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 15, 20, and 25 is 300.

Explanation:

The LCM of three non-zero integers, a(15), b(20), and c(25), is the smallest positive integer m(300) that is divisible by a(15), b(20), and c(25) without any remainder.

The methods to find the LCM of 15, 20, and 25 are explained below.

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

LCM of 15, 20, and 25 by Division Method

To calculate the LCM of 15, 20, and 25 by the division method, we will divide the numbers(15, 20, 25) by their prime factors (preferably common). The product of these divisors gives the LCM of 15, 20, and 25.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15, 20, and 25. Write this prime number(2) on the left of the given numbers(15, 20, and 25), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (15, 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 15, 20, and 25 is the product of all prime numbers on the left, i.e. LCM(15, 20, 25) by division method = 2 × 2 × 3 × 5 × 5 = 300.

LCM of 15, 20, and 25 by Listing Multiples

To calculate the LCM of 15, 20, 25 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 15 (15, 30, 45, 60, 75 . . .), 20 (20, 40, 60, 80, 100 . . .), and 25 (25, 50, 75, 100, 125 . . .).
• Step 2: The common multiples from the multiples of 15, 20, and 25 are 300, 600, . . .
• Step 3: The smallest common multiple of 15, 20, and 25 is 300.

∴ The least common multiple of 15, 20, and 25 = 300.

LCM of 15, 20, and 25 by Prime Factorization

Prime factorization of 15, 20, and 25 is (3 × 5) = 3¹ × 5¹, (2 × 2 × 5) = 2² × 5¹, and (5 × 5) = 5² respectively. LCM of 15, 20, and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5² = 300.
Hence, the LCM of 15, 20, and 25 by prime factorization is 300.

☛ Also Check:

• LCM of 10 and 35 - 70
• LCM of 8, 12 and 20 - 120
• LCM of 2, 3 and 6 - 6
• LCM of 16 and 64 - 64
• LCM of 20 and 30 - 60
• LCM of 42 and 70 - 210
• LCM of 18 and 36 - 36

FAQs on LCM of 15, 20, and 25

What is the LCM of 15, 20, and 25?

The LCM of 15, 20, and 25 is 300. To find the LCM of 15, 20, and 25, we need to find the multiples of 15, 20, and 25 (multiples of 15 = 15, 30, 45, 60 . . . . 300 . . . . ; multiples of 20 = 20, 40, 60, 80 . . . . 300 . . . . ; multiples of 25 = 25, 50, 75, 100 . . . . 300 . . . . ) and choose the smallest multiple that is exactly divisible by 15, 20, and 25, i.e., 300.

Which of the following is the LCM of 15, 20, and 25? 110, 24, 300, 42

The value of LCM of 15, 20, 25 is the smallest common multiple of 15, 20, and 25. The number satisfying the given condition is 300.

What is the Relation Between GCF and LCM of 15, 20, 25?

The following equation can be used to express the relation between GCF and LCM of 15, 20, 25, i.e. LCM(15, 20, 25) = [(15 × 20 × 25) × GCF(15, 20, 25)]/[GCF(15, 20) × GCF(20, 25) × GCF(15, 25)].

How to Find the LCM of 15, 20, and 25 by Prime Factorization?

To find the LCM of 15, 20, and 25 using prime factorization, we will find the prime factors, (15 = 3¹ × 5¹), (20 = 2² × 5¹), and (25 = 5²). LCM of 15, 20, and 25 is the product of prime factors raised to their respective highest exponent among the numbers 15, 20, and 25.
⇒ LCM of 15, 20, 25 = 2² × 3¹ × 5² = 300.