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LCM of 64 and 80

LCM of 64 and 80 is the smallest number among all common multiples of 64 and 80. The first few multiples of 64 and 80 are (64, 128, 192, 256, 320, 384, 448, . . . ) and (80, 160, 240, 320, 400, 480, 560, . . . ) respectively. There are 3 commonly used methods to find LCM of 64 and 80 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 64 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 64 and 80?

Answer: LCM of 64 and 80 is 320.

Explanation:

The LCM of two non-zero integers, x(64) and y(80), is the smallest positive integer m(320) that is divisible by both x(64) and y(80) without any remainder.

Methods to Find LCM of 64 and 80

Let's look at the different methods for finding the LCM of 64 and 80.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 64 and 80 by Division Method

To calculate the LCM of 64 and 80 by the division method, we will divide the numbers(64, 80) by their prime factors (preferably common). The product of these divisors gives the LCM of 64 and 80.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 64 and 80. Write this prime number(2) on the left of the given numbers(64 and 80), separated as per the ladder arrangement.
Step 2: If any of the given numbers (64, 80) 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 64 and 80 is the product of all prime numbers on the left, i.e. LCM(64, 80) by division method = 2 × 2 × 2 × 2 × 2 × 2 × 5 = 320.

LCM of 64 and 80 by Prime Factorization

Prime factorization of 64 and 80 is (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ and (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹ respectively. LCM of 64 and 80 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁶ × 5¹ = 320.
Hence, the LCM of 64 and 80 by prime factorization is 320.

LCM of 64 and 80 by Listing Multiples

To calculate the LCM of 64 and 80 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 64 (64, 128, 192, 256, 320, 384, 448, . . . ) and 80 (80, 160, 240, 320, 400, 480, 560, . . . . )
Step 2: The common multiples from the multiples of 64 and 80 are 320, 640, . . .
Step 3: The smallest common multiple of 64 and 80 is 320.

∴ The least common multiple of 64 and 80 = 320.

☛ Also Check:

LCM of 64 and 80 Examples

Example 1: The product of two numbers is 5120. If their GCD is 16, what is their LCM?

Solution:

Given: GCD = 16
product of numbers = 5120
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 5120/16
Therefore, the LCM is 320.
The probable combination for the given case is LCM(64, 80) = 320.
Example 2: Find the smallest number that is divisible by 64 and 80 exactly.

Solution:

The smallest number that is divisible by 64 and 80 exactly is their LCM.
⇒ Multiples of 64 and 80:
- Multiples of 64 = 64, 128, 192, 256, 320, . . . .
- Multiples of 80 = 80, 160, 240, 320, 400, . . . .
Therefore, the LCM of 64 and 80 is 320.
Example 3: Verify the relationship between GCF and LCM of 64 and 80.

Solution:

The relation between GCF and LCM of 64 and 80 is given as,
LCM(64, 80) × GCF(64, 80) = Product of 64, 80
Prime factorization of 64 and 80 is given as, 64 = (2 × 2 × 2 × 2 × 2 × 2) = 2⁶ and 80 = (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹
LCM(64, 80) = 320
GCF(64, 80) = 16
LHS = LCM(64, 80) × GCF(64, 80) = 320 × 16 = 5120
RHS = Product of 64, 80 = 64 × 80 = 5120
⇒ LHS = RHS = 5120
Hence, verified.

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FAQs on LCM of 64 and 80

What is the LCM of 64 and 80?

The LCM of 64 and 80 is 320. To find the LCM (least common multiple) of 64 and 80, we need to find the multiples of 64 and 80 (multiples of 64 = 64, 128, 192, 256 . . . . 320; multiples of 80 = 80, 160, 240, 320) and choose the smallest multiple that is exactly divisible by 64 and 80, i.e., 320.

How to Find the LCM of 64 and 80 by Prime Factorization?

To find the LCM of 64 and 80 using prime factorization, we will find the prime factors, (64 = 2 × 2 × 2 × 2 × 2 × 2) and (80 = 2 × 2 × 2 × 2 × 5). LCM of 64 and 80 is the product of prime factors raised to their respective highest exponent among the numbers 64 and 80.
⇒ LCM of 64, 80 = 2⁶ × 5¹ = 320.

If the LCM of 80 and 64 is 320, Find its GCF.

LCM(80, 64) × GCF(80, 64) = 80 × 64
Since the LCM of 80 and 64 = 320
⇒ 320 × GCF(80, 64) = 5120
Therefore, the greatest common factor (GCF) = 5120/320 = 16.

Which of the following is the LCM of 64 and 80? 18, 320, 11, 3

The value of LCM of 64, 80 is the smallest common multiple of 64 and 80. The number satisfying the given condition is 320.

What is the Relation Between GCF and LCM of 64, 80?

The following equation can be used to express the relation between GCF and LCM of 64 and 80, i.e. GCF × LCM = 64 × 80.

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