LCM of 3 and 15

LCM of 3 and 15 is the smallest number among all common multiples of 3 and 15. The first few multiples of 3 and 15 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (15, 30, 45, 60, 75, 90, 105, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 15 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 3 and 15 is 15.

Explanation:

The LCM of two non-zero integers, x(3) and y(15), is the smallest positive integer m(15) that is divisible by both x(3) and y(15) without any remainder.

The methods to find the LCM of 3 and 15 are explained below.

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

LCM of 3 and 15 by Division Method

To calculate the LCM of 3 and 15 by the division method, we will divide the numbers(3, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 15.

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

LCM of 3 and 15 by Listing Multiples

To calculate the LCM of 3 and 15 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 15 (15, 30, 45, 60, 75, 90, 105, . . . . )
• Step 2: The common multiples from the multiples of 3 and 15 are 15, 30, . . .
• Step 3: The smallest common multiple of 3 and 15 is 15.

∴ The least common multiple of 3 and 15 = 15.

LCM of 3 and 15 by Prime Factorization

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

☛ Also Check:

• LCM of 14 and 91 - 182
• LCM of 5, 6 and 7 - 210
• LCM of 4, 8 and 12 - 24
• LCM of 21 and 27 - 189
• LCM of 12, 15 and 18 - 180
• LCM of 16 and 64 - 64
• LCM of 25 and 16 - 400

FAQs on LCM of 3 and 15

What is the LCM of 3 and 15?

The LCM of 3 and 15 is 15. To find the LCM of 3 and 15, we need to find the multiples of 3 and 15 (multiples of 3 = 3, 6, 9, 12 . . . . 15; multiples of 15 = 15, 30, 45, 60) and choose the smallest multiple that is exactly divisible by 3 and 15, i.e., 15.

What is the Relation Between GCF and LCM of 3, 15?

The following equation can be used to express the relation between GCF and LCM of 3 and 15, i.e. GCF × LCM = 3 × 15.

If the LCM of 15 and 3 is 15, Find its GCF.

LCM(15, 3) × GCF(15, 3) = 15 × 3
Since the LCM of 15 and 3 = 15
⇒ 15 × GCF(15, 3) = 45
Therefore, the greatest common factor = 45/15 = 3.

How to Find the LCM of 3 and 15 by Prime Factorization?

To find the LCM of 3 and 15 using prime factorization, we will find the prime factors, (3 = 3) and (15 = 3 × 5). LCM of 3 and 15 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 15.
⇒ LCM of 3, 15 = 3¹ × 5¹ = 15.

What are the Methods to Find LCM of 3 and 15?

The commonly used methods to find the LCM of 3 and 15 are:

• Listing Multiples
• Prime Factorization Method
• Division Method