LCM of 50 and 48

LCM of 50 and 48 is the smallest number among all common multiples of 50 and 48. The first few multiples of 50 and 48 are (50, 100, 150, 200, 250, 300, . . . ) and (48, 96, 144, 192, 240, 288, 336, . . . ) respectively. There are 3 commonly used methods to find LCM of 50 and 48 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 50 and 48 is 1200.

Explanation:

The LCM of two non-zero integers, x(50) and y(48), is the smallest positive integer m(1200) that is divisible by both x(50) and y(48) without any remainder.

Let's look at the different methods for finding the LCM of 50 and 48.

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

LCM of 50 and 48 by Listing Multiples

To calculate the LCM of 50 and 48 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 50 (50, 100, 150, 200, 250, 300, . . . ) and 48 (48, 96, 144, 192, 240, 288, 336, . . . . )
• Step 2: The common multiples from the multiples of 50 and 48 are 1200, 2400, . . .
• Step 3: The smallest common multiple of 50 and 48 is 1200.

∴ The least common multiple of 50 and 48 = 1200.

LCM of 50 and 48 by Division Method

To calculate the LCM of 50 and 48 by the division method, we will divide the numbers(50, 48) by their prime factors (preferably common). The product of these divisors gives the LCM of 50 and 48.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 50 and 48. Write this prime number(2) on the left of the given numbers(50 and 48), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (50, 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 50 and 48 is the product of all prime numbers on the left, i.e. LCM(50, 48) by division method = 2 × 2 × 2 × 2 × 3 × 5 × 5 = 1200.

LCM of 50 and 48 by Prime Factorization

Prime factorization of 50 and 48 is (2 × 5 × 5) = 2¹ × 5² and (2 × 2 × 2 × 2 × 3) = 2⁴ × 3¹ respectively. LCM of 50 and 48 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5² = 1200.
Hence, the LCM of 50 and 48 by prime factorization is 1200.

☛ Also Check:

• LCM of 15 and 16 - 240
• LCM of 15, 30 and 90 - 90
• LCM of 3 and 12 - 12
• LCM of 3, 4 and 8 - 24
• LCM of 4, 12 and 16 - 48
• LCM of 75 and 105 - 525
• LCM of 120 and 90 - 360

FAQs on LCM of 50 and 48

What is the LCM of 50 and 48?

The LCM of 50 and 48 is 1200. To find the LCM of 50 and 48, we need to find the multiples of 50 and 48 (multiples of 50 = 50, 100, 150, 200 . . . . 1200; multiples of 48 = 48, 96, 144, 192 . . . . 1200) and choose the smallest multiple that is exactly divisible by 50 and 48, i.e., 1200.

Which of the following is the LCM of 50 and 48? 20, 1200, 16, 27

The value of LCM of 50, 48 is the smallest common multiple of 50 and 48. The number satisfying the given condition is 1200.

What are the Methods to Find LCM of 50 and 48?

The commonly used methods to find the LCM of 50 and 48 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 48 and 50 is 1200, Find its GCF.

LCM(48, 50) × GCF(48, 50) = 48 × 50
Since the LCM of 48 and 50 = 1200
⇒ 1200 × GCF(48, 50) = 2400
Therefore, the greatest common factor (GCF) = 2400/1200 = 2.

What is the Least Perfect Square Divisible by 50 and 48?

The least number divisible by 50 and 48 = LCM(50, 48)
LCM of 50 and 48 = 2 × 2 × 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 50 and 48 = LCM(50, 48) × 3 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.