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LCM of 850 and 680

LCM of 850 and 680 is the smallest number among all common multiples of 850 and 680. The first few multiples of 850 and 680 are (850, 1700, 2550, 3400, 4250, . . . ) and (680, 1360, 2040, 2720, . . . ) respectively. There are 3 commonly used methods to find LCM of 850 and 680 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 850 and 680
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 850 and 680?

Answer: LCM of 850 and 680 is 3400.

Explanation:

The LCM of two non-zero integers, x(850) and y(680), is the smallest positive integer m(3400) that is divisible by both x(850) and y(680) without any remainder.

Methods to Find LCM of 850 and 680

Let's look at the different methods for finding the LCM of 850 and 680.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 850 and 680 by Division Method

To calculate the LCM of 850 and 680 by the division method, we will divide the numbers(850, 680) by their prime factors (preferably common). The product of these divisors gives the LCM of 850 and 680.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 850 and 680. Write this prime number(2) on the left of the given numbers(850 and 680), separated as per the ladder arrangement.
Step 2: If any of the given numbers (850, 680) 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 850 and 680 is the product of all prime numbers on the left, i.e. LCM(850, 680) by division method = 2 × 2 × 2 × 5 × 5 × 17 = 3400.

LCM of 850 and 680 by Listing Multiples

To calculate the LCM of 850 and 680 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 850 (850, 1700, 2550, 3400, 4250, . . . ) and 680 (680, 1360, 2040, 2720, . . . . )
Step 2: The common multiples from the multiples of 850 and 680 are 3400, 6800, . . .
Step 3: The smallest common multiple of 850 and 680 is 3400.

∴ The least common multiple of 850 and 680 = 3400.

LCM of 850 and 680 by Prime Factorization

Prime factorization of 850 and 680 is (2 × 5 × 5 × 17) = 2¹ × 5² × 17¹ and (2 × 2 × 2 × 5 × 17) = 2³ × 5¹ × 17¹ respectively. LCM of 850 and 680 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5² × 17¹ = 3400.
Hence, the LCM of 850 and 680 by prime factorization is 3400.

☛ Also Check:

LCM of 850 and 680 Examples

Example 1: The GCD and LCM of two numbers are 170 and 3400 respectively. If one number is 850, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 850 × a
⇒ a = (GCD × LCM)/850
⇒ a = (170 × 3400)/850
⇒ a = 680
Therefore, the other number is 680.
Example 2: Find the smallest number that is divisible by 850 and 680 exactly.

Solution:

The smallest number that is divisible by 850 and 680 exactly is their LCM.
⇒ Multiples of 850 and 680:
- Multiples of 850 = 850, 1700, 2550, 3400, 4250, 5100, 5950, . . . .
- Multiples of 680 = 680, 1360, 2040, 2720, 3400, 4080, 4760, . . . .
Therefore, the LCM of 850 and 680 is 3400.
Example 3: The product of two numbers is 578000. If their GCD is 170, what is their LCM?

Solution:

Given: GCD = 170
product of numbers = 578000
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 578000/170
Therefore, the LCM is 3400.
The probable combination for the given case is LCM(850, 680) = 3400.

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FAQs on LCM of 850 and 680

What is the LCM of 850 and 680?

The LCM of 850 and 680 is 3400. To find the LCM (least common multiple) of 850 and 680, we need to find the multiples of 850 and 680 (multiples of 850 = 850, 1700, 2550, 3400; multiples of 680 = 680, 1360, 2040, 2720 . . . . 3400) and choose the smallest multiple that is exactly divisible by 850 and 680, i.e., 3400.

Which of the following is the LCM of 850 and 680? 3400, 32, 27, 11

The value of LCM of 850, 680 is the smallest common multiple of 850 and 680. The number satisfying the given condition is 3400.

How to Find the LCM of 850 and 680 by Prime Factorization?

To find the LCM of 850 and 680 using prime factorization, we will find the prime factors, (850 = 2 × 5 × 5 × 17) and (680 = 2 × 2 × 2 × 5 × 17). LCM of 850 and 680 is the product of prime factors raised to their respective highest exponent among the numbers 850 and 680.
⇒ LCM of 850, 680 = 2³ × 5² × 17¹ = 3400.

What is the Least Perfect Square Divisible by 850 and 680?

The least number divisible by 850 and 680 = LCM(850, 680)
LCM of 850 and 680 = 2 × 2 × 2 × 5 × 5 × 17 [Incomplete pair(s): 2, 17]
⇒ Least perfect square divisible by each 850 and 680 = LCM(850, 680) × 2 × 17 = 115600 [Square root of 115600 = √115600 = ±340]
Therefore, 115600 is the required number.

If the LCM of 680 and 850 is 3400, Find its GCF.

LCM(680, 850) × GCF(680, 850) = 680 × 850
Since the LCM of 680 and 850 = 3400
⇒ 3400 × GCF(680, 850) = 578000
Therefore, the GCF = 578000/3400 = 170.

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