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LCM of 16, 28, 40, and 77

LCM of 16, 28, 40, and 77 is the smallest number among all common multiples of 16, 28, 40, and 77. The first few multiples of 16, 28, 40, and 77 are (16, 32, 48, 64, 80 . . .), (28, 56, 84, 112, 140 . . .), (40, 80, 120, 160, 200 . . .), and (77, 154, 231, 308, 385 . . .) respectively. There are 3 commonly used methods to find LCM of 16, 28, 40, 77 - by prime factorization, by division method, and by listing multiples.

1.	LCM of 16, 28, 40, and 77
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 16, 28, 40, and 77?

Answer: LCM of 16, 28, 40, and 77 is 6160.

Explanation:

The LCM of four non-zero integers, a(16), b(28), c(40), and d(77), is the smallest positive integer m(6160) that is divisible by a(16), b(28), c(40), and d(77) without any remainder.

Methods to Find LCM of 16, 28, 40, and 77

The methods to find the LCM of 16, 28, 40, and 77 are explained below.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 16, 28, 40, and 77 by Listing Multiples

To calculate the LCM of 16, 28, 40, 77 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 16 (16, 32, 48, 64, 80 . . .), 28 (28, 56, 84, 112, 140 . . .), 40 (40, 80, 120, 160, 200 . . .), and 77 (77, 154, 231, 308, 385 . . .).
Step 2: The common multiples from the multiples of 16, 28, 40, and 77 are 6160, 12320, . . .
Step 3: The smallest common multiple of 16, 28, 40, and 77 is 6160.

∴ The least common multiple of 16, 28, 40, and 77 = 6160.

LCM of 16, 28, 40, and 77 by Prime Factorization

Prime factorization of 16, 28, 40, and 77 is (2 × 2 × 2 × 2) = 2⁴, (2 × 2 × 7) = 2² × 7¹, (2 × 2 × 2 × 5) = 2³ × 5¹, and (7 × 11) = 7¹ × 11¹ respectively. LCM of 16, 28, 40, and 77 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 5¹ × 7¹ × 11¹ = 6160.
Hence, the LCM of 16, 28, 40, and 77 by prime factorization is 6160.

LCM of 16, 28, 40, and 77 by Division Method

To calculate the LCM of 16, 28, 40, and 77 by the division method, we will divide the numbers(16, 28, 40, 77) by their prime factors (preferably common). The product of these divisors gives the LCM of 16, 28, 40, and 77.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16, 28, 40, and 77. Write this prime number(2) on the left of the given numbers(16, 28, 40, and 77), separated as per the ladder arrangement.
Step 2: If any of the given numbers (16, 28, 40, 77) 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 16, 28, 40, and 77 is the product of all prime numbers on the left, i.e. LCM(16, 28, 40, 77) by division method = 2 × 2 × 2 × 2 × 5 × 7 × 11 = 6160.

☛ Also Check:

LCM of 16, 28, 40, and 77 Examples

Example 1: Which of the following is the LCM of 16, 28, 40, 77? 42, 6160, 18, 15.

Solution:

The value of LCM of 16, 28, 40, and 77 is the smallest common multiple of 16, 28, 40, and 77. The number satisfying the given condition is 6160. ∴LCM(16, 28, 40, 77) = 6160.
Example 2: Find the smallest number which when divided by 16, 28, 40, and 77 leaves 6 as the remainder in each case.

Solution:

The smallest number exactly divisible by 16, 28, 40, and 77 = LCM(16, 28, 40, 77) ⇒ Smallest number which leaves 6 as remainder when divided by 16, 28, 40, and 77 = LCM(16, 28, 40, 77) + 6
- 16 = 2⁴
- 28 = 2² × 7¹
- 40 = 2³ × 5¹
- 77 = 7¹ × 11¹
LCM(16, 28, 40, 77) = 2⁴ × 5¹ × 7¹ × 11¹ = 6160
⇒ The required number = 6160 + 6 = 6166.
Example 3: Find the smallest number that is divisible by 16, 28, 40, 77 exactly.

Solution:

The value of LCM(16, 28, 40, 77) will be the smallest number that is exactly divisible by 16, 28, 40, and 77.
⇒ Multiples of 16, 28, 40, and 77:
- Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, . . . ., 6096, 6112, 6128, 6144, 6160, . . . .
- Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, . . . ., 6104, 6132, 6160, . . . .
- Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 6000, 6040, 6080, 6120, 6160, . . . .
- Multiples of 77 = 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, . . . ., 5929, 6006, 6083, 6160, . . . .
Therefore, the LCM of 16, 28, 40, and 77 is 6160.

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FAQs on LCM of 16, 28, 40, and 77

What is the LCM of 16, 28, 40, and 77?

The LCM of 16, 28, 40, and 77 is 6160. To find the LCM of 16, 28, 40, and 77, we need to find the multiples of 16, 28, 40, and 77 (multiples of 16 = 16, 32, 48, 64 . . . . 6160 . . . . ; multiples of 28 = 28, 56, 84, 112 . . . . 6160 . . . . ; multiples of 40 = 40, 80, 120, 160 . . . . 6160 . . . . ; multiples of 77 = 77, 154, 231, 308 . . . . 6160 . . . . ) and choose the smallest multiple that is exactly divisible by 16, 28, 40, and 77, i.e., 6160.

What is the Least Perfect Square Divisible by 16, 28, 40, and 77?

The least number divisible by 16, 28, 40, and 77 = LCM(16, 28, 40, 77)
LCM of 16, 28, 40, and 77 = 2 × 2 × 2 × 2 × 5 × 7 × 11 [Incomplete pair(s): 5, 7, 11]
⇒ Least perfect square divisible by each 16, 28, 40, and 77 = LCM(16, 28, 40, 77) × 5 × 7 × 11 = 2371600 [Square root of 2371600 = √2371600 = ±1540]
Therefore, 2371600 is the required number.

Which of the following is the LCM of 16, 28, 40, and 77? 6160, 18, 20, 3

The value of LCM of 16, 28, 40, 77 is the smallest common multiple of 16, 28, 40, and 77. The number satisfying the given condition is 6160.

What are the Methods to Find LCM of 16, 28, 40, 77?

The commonly used methods to find the LCM of 16, 28, 40, 77 are:

Listing Multiples
Prime Factorization Method
Division Method

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