LCM of 404 and 96

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

Answer: LCM of 404 and 96 is 9696.

Explanation:

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

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

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

LCM of 404 and 96 by Division Method

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

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

LCM of 404 and 96 by Listing Multiples

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

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

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

LCM of 404 and 96 by Prime Factorization

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

☛ Also Check:

• LCM of 72 and 84 - 504
• LCM of 10, 20 and 25 - 100
• LCM of 12, 16, 24 and 36 - 144
• LCM of 5, 10 and 15 - 30
• LCM of 24, 15 and 36 - 360
• LCM of 22 and 33 - 66
• LCM of 30 and 75 - 150

FAQs on LCM of 404 and 96

What is the LCM of 404 and 96?

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

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

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

Which of the following is the LCM of 404 and 96? 16, 2, 10, 9696

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

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

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

How to Find the LCM of 404 and 96 by Prime Factorization?

To find the LCM of 404 and 96 using prime factorization, we will find the prime factors, (404 = 2 × 2 × 101) and (96 = 2 × 2 × 2 × 2 × 2 × 3). LCM of 404 and 96 is the product of prime factors raised to their respective highest exponent among the numbers 404 and 96.
⇒ LCM of 404, 96 = 2⁵ × 3¹ × 101¹ = 9696.