LCM of 96 and 404

LCM of 96 and 404 is the smallest number among all common multiples of 96 and 404. The first few multiples of 96 and 404 are (96, 192, 288, 384, 480, 576, 672, . . . ) and (404, 808, 1212, 1616, . . . ) respectively. There are 3 commonly used methods to find LCM of 96 and 404 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 96 and 404 is 9696.

Explanation:

The LCM of two non-zero integers, x(96) and y(404), is the smallest positive integer m(9696) that is divisible by both x(96) and y(404) without any remainder.

Let's look at the different methods for finding the LCM of 96 and 404.

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

LCM of 96 and 404 by Division Method

To calculate the LCM of 96 and 404 by the division method, we will divide the numbers(96, 404) by their prime factors (preferably common). The product of these divisors gives the LCM of 96 and 404.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 96 and 404. Write this prime number(2) on the left of the given numbers(96 and 404), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (96, 404) 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 96 and 404 is the product of all prime numbers on the left, i.e. LCM(96, 404) by division method = 2 × 2 × 2 × 2 × 2 × 3 × 101 = 9696.

LCM of 96 and 404 by Listing Multiples

To calculate the LCM of 96 and 404 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 96 (96, 192, 288, 384, 480, 576, 672, . . . ) and 404 (404, 808, 1212, 1616, . . . . )
• Step 2: The common multiples from the multiples of 96 and 404 are 9696, 19392, . . .
• Step 3: The smallest common multiple of 96 and 404 is 9696.

∴ The least common multiple of 96 and 404 = 9696.

LCM of 96 and 404 by Prime Factorization

Prime factorization of 96 and 404 is (2 × 2 × 2 × 2 × 2 × 3) = 2⁵ × 3¹ and (2 × 2 × 101) = 2² × 101¹ respectively. LCM of 96 and 404 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 3¹ × 101¹ = 9696.
Hence, the LCM of 96 and 404 by prime factorization is 9696.

☛ Also Check:

• LCM of 8 and 42 - 168
• LCM of 5, 6 and 9 - 90
• LCM of 20 and 32 - 160
• LCM of 56 and 84 - 168
• LCM of 24 and 8 - 24
• LCM of 3, 5 and 11 - 165
• LCM of 27 and 81 - 81

FAQs on LCM of 96 and 404

What is the LCM of 96 and 404?

The LCM of 96 and 404 is 9696. To find the least common multiple (LCM) of 96 and 404, we need to find the multiples of 96 and 404 (multiples of 96 = 96, 192, 288, 384 . . . . 9696; multiples of 404 = 404, 808, 1212, 1616 . . . . 9696) and choose the smallest multiple that is exactly divisible by 96 and 404, i.e., 9696.

What is the Least Perfect Square Divisible by 96 and 404?

The least number divisible by 96 and 404 = LCM(96, 404)
LCM of 96 and 404 = 2 × 2 × 2 × 2 × 2 × 3 × 101 [Incomplete pair(s): 2, 3, 101]
⇒ Least perfect square divisible by each 96 and 404 = LCM(96, 404) × 2 × 3 × 101 = 5875776 [Square root of 5875776 = √5875776 = ±2424]
Therefore, 5875776 is the required number.

If the LCM of 404 and 96 is 9696, Find its GCF.

LCM(404, 96) × GCF(404, 96) = 404 × 96
Since the LCM of 404 and 96 = 9696
⇒ 9696 × GCF(404, 96) = 38784
Therefore, the greatest common factor = 38784/9696 = 4.

What are the Methods to Find LCM of 96 and 404?

The commonly used methods to find the LCM of 96 and 404 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

Which of the following is the LCM of 96 and 404? 18, 9696, 30, 50

The value of LCM of 96, 404 is the smallest common multiple of 96 and 404. The number satisfying the given condition is 9696.