LCM of 8 and 48

LCM of 8 and 48 is the smallest number among all common multiples of 8 and 48. The first few multiples of 8 and 48 are (8, 16, 24, 32, 40, 48, 56, . . . ) and (48, 96, 144, 192, 240, 288, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 48 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 8 and 48 is 48.

Explanation:

The LCM of two non-zero integers, x(8) and y(48), is the smallest positive integer m(48) that is divisible by both x(8) and y(48) without any remainder.

The methods to find the LCM of 8 and 48 are explained below.

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

LCM of 8 and 48 by Prime Factorization

Prime factorization of 8 and 48 is (2 × 2 × 2) = 2³ and (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ respectively. LCM of 8 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ = 48.
Hence, the LCM of 8 and 48 by prime factorization is 48.

LCM of 8 and 48 by Listing Multiples

To calculate the LCM of 8 and 48 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, 40, 48, 56, . . . ) and 48 (48, 96, 144, 192, 240, 288, . . . . )
• Step 2: The common multiples from the multiples of 8 and 48 are 48, 96, . . .
• Step 3: The smallest common multiple of 8 and 48 is 48.

∴ The least common multiple of 8 and 48 = 48.

LCM of 8 and 48 by Division Method

To calculate the LCM of 8 and 48 by the division method, we will divide the numbers(8, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 48.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 48. Write this prime number(2) on the left of the given numbers(8 and 48), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 48) 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 48 is the product of all prime numbers on the left, i.e. LCM(8, 48) by division method = 2 × 2 × 2 × 2 × 3 = 48.

☛ Also Check:

• LCM of 32 and 36 - 288
• LCM of 5 and 25 - 25
• LCM of 6, 7 and 8 - 168
• LCM of 45 and 50 - 450
• LCM of 2 and 15 - 30
• LCM of 18 and 36 - 36
• LCM of 45 and 120 - 360

FAQs on LCM of 8 and 48

What is the LCM of 8 and 48?

The LCM of 8 and 48 is 48. To find the least common multiple of 8 and 48, we need to find the multiples of 8 and 48 (multiples of 8 = 8, 16, 24, 32 . . . . 48; multiples of 48 = 48, 96, 144, 192) and choose the smallest multiple that is exactly divisible by 8 and 48, i.e., 48.

What is the Least Perfect Square Divisible by 8 and 48?

The least number divisible by 8 and 48 = LCM(8, 48)
LCM of 8 and 48 = 2 × 2 × 2 × 2 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 8 and 48 = LCM(8, 48) × 3 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

If the LCM of 48 and 8 is 48, Find its GCF.

LCM(48, 8) × GCF(48, 8) = 48 × 8
Since the LCM of 48 and 8 = 48
⇒ 48 × GCF(48, 8) = 384
Therefore, the GCF (greatest common factor) = 384/48 = 8.

What are the Methods to Find LCM of 8 and 48?

The commonly used methods to find the LCM of 8 and 48 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

How to Find the LCM of 8 and 48 by Prime Factorization?

To find the LCM of 8 and 48 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (48 = 2 × 2 × 2 × 2 × 3). LCM of 8 and 48 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 48.
⇒ LCM of 8, 48 = 2⁴ × 3¹ = 48.