LCM of 48 and 120

LCM of 48 and 120 is the smallest number among all common multiples of 48 and 120. The first few multiples of 48 and 120 are (48, 96, 144, 192, 240, 288, . . . ) and (120, 240, 360, 480, 600, . . . ) respectively. There are 3 commonly used methods to find LCM of 48 and 120 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 48 and 120 is 240.

Explanation:

The LCM of two non-zero integers, x(48) and y(120), is the smallest positive integer m(240) that is divisible by both x(48) and y(120) without any remainder.

The methods to find the LCM of 48 and 120 are explained below.

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

LCM of 48 and 120 by Listing Multiples

To calculate the LCM of 48 and 120 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 48 (48, 96, 144, 192, 240, 288, . . . ) and 120 (120, 240, 360, 480, 600, . . . . )
• Step 2: The common multiples from the multiples of 48 and 120 are 240, 480, . . .
• Step 3: The smallest common multiple of 48 and 120 is 240.

∴ The least common multiple of 48 and 120 = 240.

LCM of 48 and 120 by Division Method

To calculate the LCM of 48 and 120 by the division method, we will divide the numbers(48, 120) by their prime factors (preferably common). The product of these divisors gives the LCM of 48 and 120.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 48 and 120. Write this prime number(2) on the left of the given numbers(48 and 120), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (48, 120) 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 48 and 120 is the product of all prime numbers on the left, i.e. LCM(48, 120) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

LCM of 48 and 120 by Prime Factorization

Prime factorization of 48 and 120 is (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ and (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ respectively. LCM of 48 and 120 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5¹ = 240.
Hence, the LCM of 48 and 120 by prime factorization is 240.

☛ Also Check:

• LCM of 12, 16 and 20 - 240
• LCM of 11 and 15 - 165
• LCM of 6 and 10 - 30
• LCM of 36 and 63 - 252
• LCM of 30, 36 and 40 - 360
• LCM of 25 and 75 - 75
• LCM of 16 and 32 - 32

FAQs on LCM of 48 and 120

What is the LCM of 48 and 120?

The LCM of 48 and 120 is 240. To find the LCM (least common multiple) of 48 and 120, we need to find the multiples of 48 and 120 (multiples of 48 = 48, 96, 144, 192 . . . . 240; multiples of 120 = 120, 240, 360, 480) and choose the smallest multiple that is exactly divisible by 48 and 120, i.e., 240.

How to Find the LCM of 48 and 120 by Prime Factorization?

To find the LCM of 48 and 120 using prime factorization, we will find the prime factors, (48 = 2 × 2 × 2 × 2 × 3) and (120 = 2 × 2 × 2 × 3 × 5). LCM of 48 and 120 is the product of prime factors raised to their respective highest exponent among the numbers 48 and 120.
⇒ LCM of 48, 120 = 2⁴ × 3¹ × 5¹ = 240.

If the LCM of 120 and 48 is 240, Find its GCF.

LCM(120, 48) × GCF(120, 48) = 120 × 48
Since the LCM of 120 and 48 = 240
⇒ 240 × GCF(120, 48) = 5760
Therefore, the greatest common factor (GCF) = 5760/240 = 24.

Which of the following is the LCM of 48 and 120? 25, 3, 15, 240

The value of LCM of 48, 120 is the smallest common multiple of 48 and 120. The number satisfying the given condition is 240.

What is the Least Perfect Square Divisible by 48 and 120?

The least number divisible by 48 and 120 = LCM(48, 120)
LCM of 48 and 120 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 48 and 120 = LCM(48, 120) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.