LCM of 8 and 15

LCM of 8 and 15 is the smallest number among all common multiples of 8 and 15. The first few multiples of 8 and 15 are (8, 16, 24, 32, . . . ) and (15, 30, 45, 60, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 15 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 8 and 15 is 120.

Explanation:

The LCM of two non-zero integers, x(8) and y(15), is the smallest positive integer m(120) that is divisible by both x(8) and y(15) without any remainder.

The methods to find the LCM of 8 and 15 are explained below.

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

LCM of 8 and 15 by Division Method

To calculate the LCM of 8 and 15 by the division method, we will divide the numbers(8, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 15.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 15. Write this prime number(2) on the left of the given numbers(8 and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 15) 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 and 15 is the product of all prime numbers on the left, i.e. LCM(8, 15) by division method = 2 × 2 × 2 × 3 × 5 = 120.

LCM of 8 and 15 by Listing Multiples

To calculate the LCM of 8 and 15 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, . . . ) and 15 (15, 30, 45, 60, . . . . )
• Step 2: The common multiples from the multiples of 8 and 15 are 120, 240, . . .
• Step 3: The smallest common multiple of 8 and 15 is 120.

∴ The least common multiple of 8 and 15 = 120.

LCM of 8 and 15 by Prime Factorization

Prime factorization of 8 and 15 is (2 × 2 × 2) = 2³ and (3 × 5) = 3¹ × 5¹ respectively. LCM of 8 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5¹ = 120.
Hence, the LCM of 8 and 15 by prime factorization is 120.

☛ Also Check:

• LCM of 14 and 49 - 98
• LCM of 27 and 63 - 189
• LCM of 8 and 42 - 168
• LCM of 3 and 6 - 6
• LCM of 3 and 13 - 39
• LCM of 105 and 195 - 1365
• LCM of 20 and 35 - 140

FAQs on LCM of 8 and 15

What is the LCM of 8 and 15?

The LCM of 8 and 15 is 120. To find the least common multiple of 8 and 15, we need to find the multiples of 8 and 15 (multiples of 8 = 8, 16, 24, 32 . . . . 120; multiples of 15 = 15, 30, 45, 60 . . . . 120) and choose the smallest multiple that is exactly divisible by 8 and 15, i.e., 120.

If the LCM of 15 and 8 is 120, Find its GCF.

LCM(15, 8) × GCF(15, 8) = 15 × 8
Since the LCM of 15 and 8 = 120
⇒ 120 × GCF(15, 8) = 120
Therefore, the greatest common factor = 120/120 = 1.

How to Find the LCM of 8 and 15 by Prime Factorization?

To find the LCM of 8 and 15 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (15 = 3 × 5). LCM of 8 and 15 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 15.
⇒ LCM of 8, 15 = 2³ × 3¹ × 5¹ = 120.

What is the Least Perfect Square Divisible by 8 and 15?

The least number divisible by 8 and 15 = LCM(8, 15)
LCM of 8 and 15 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 8 and 15 = LCM(8, 15) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

Which of the following is the LCM of 8 and 15? 120, 50, 15, 18

The value of LCM of 8, 15 is the smallest common multiple of 8 and 15. The number satisfying the given condition is 120.