LCM of 15 and 16

LCM of 15 and 16 is the smallest number among all common multiples of 15 and 16. The first few multiples of 15 and 16 are (15, 30, 45, 60, . . . ) and (16, 32, 48, 64, 80, 96, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 16 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 15 and 16 is 240.

Explanation:

The LCM of two non-zero integers, x(15) and y(16), is the smallest positive integer m(240) that is divisible by both x(15) and y(16) without any remainder.

The methods to find the LCM of 15 and 16 are explained below.

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

LCM of 15 and 16 by Listing Multiples

To calculate the LCM of 15 and 16 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, . . . ) and 16 (16, 32, 48, 64, 80, 96, 112, . . . . )
• Step 2: The common multiples from the multiples of 15 and 16 are 240, 480, . . .
• Step 3: The smallest common multiple of 15 and 16 is 240.

∴ The least common multiple of 15 and 16 = 240.

LCM of 15 and 16 by Prime Factorization

Prime factorization of 15 and 16 is (3 × 5) = 3¹ × 5¹ and (2 × 2 × 2 × 2) = 2⁴ respectively. LCM of 15 and 16 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5¹ = 240.
Hence, the LCM of 15 and 16 by prime factorization is 240.

LCM of 15 and 16 by Division Method

To calculate the LCM of 15 and 16 by the division method, we will divide the numbers(15, 16) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 16.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 16. Write this prime number(2) on the left of the given numbers(15 and 16), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (15, 16) 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 and 16 is the product of all prime numbers on the left, i.e. LCM(15, 16) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

☛ Also Check:

• LCM of 42 and 63 - 126
• LCM of 42 and 56 - 168
• LCM of 42 and 48 - 336
• LCM of 404 and 96 - 9696
• LCM of 40 and 60 - 120
• LCM of 40 and 56 - 280
• LCM of 40 and 50 - 200

FAQs on LCM of 15 and 16

What is the LCM of 15 and 16?

The LCM of 15 and 16 is 240. To find the LCM of 15 and 16, we need to find the multiples of 15 and 16 (multiples of 15 = 15, 30, 45, 60 . . . . 240; multiples of 16 = 16, 32, 48, 64 . . . . 240) and choose the smallest multiple that is exactly divisible by 15 and 16, i.e., 240.

What are the Methods to Find LCM of 15 and 16?

The commonly used methods to find the LCM of 15 and 16 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

If the LCM of 16 and 15 is 240, Find its GCF.

LCM(16, 15) × GCF(16, 15) = 16 × 15
Since the LCM of 16 and 15 = 240
⇒ 240 × GCF(16, 15) = 240
Therefore, the greatest common factor (GCF) = 240/240 = 1.

How to Find the LCM of 15 and 16 by Prime Factorization?

To find the LCM of 15 and 16 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (16 = 2 × 2 × 2 × 2). LCM of 15 and 16 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 16.
⇒ LCM of 15, 16 = 2⁴ × 3¹ × 5¹ = 240.

Which of the following is the LCM of 15 and 16? 32, 3, 40, 240

The value of LCM of 15, 16 is the smallest common multiple of 15 and 16. The number satisfying the given condition is 240.