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LCM of 32 and 80

LCM of 32 and 80 is the smallest number among all common multiples of 32 and 80. The first few multiples of 32 and 80 are (32, 64, 96, 128, 160, 192, 224, . . . ) and (80, 160, 240, 320, 400, . . . ) respectively. There are 3 commonly used methods to find LCM of 32 and 80 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 32 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 32 and 80?

Answer: LCM of 32 and 80 is 160.

Explanation:

The LCM of two non-zero integers, x(32) and y(80), is the smallest positive integer m(160) that is divisible by both x(32) and y(80) without any remainder.

Methods to Find LCM of 32 and 80

The methods to find the LCM of 32 and 80 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 32 and 80 by Prime Factorization

Prime factorization of 32 and 80 is (2 × 2 × 2 × 2 × 2) = 2⁵ and (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹ respectively. LCM of 32 and 80 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 5¹ = 160.
Hence, the LCM of 32 and 80 by prime factorization is 160.

LCM of 32 and 80 by Listing Multiples

To calculate the LCM of 32 and 80 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 32 (32, 64, 96, 128, 160, 192, 224, . . . ) and 80 (80, 160, 240, 320, 400, . . . . )
Step 2: The common multiples from the multiples of 32 and 80 are 160, 320, . . .
Step 3: The smallest common multiple of 32 and 80 is 160.

∴ The least common multiple of 32 and 80 = 160.

LCM of 32 and 80 by Division Method

To calculate the LCM of 32 and 80 by the division method, we will divide the numbers(32, 80) by their prime factors (preferably common). The product of these divisors gives the LCM of 32 and 80.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 32 and 80. Write this prime number(2) on the left of the given numbers(32 and 80), separated as per the ladder arrangement.
Step 2: If any of the given numbers (32, 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 32 and 80 is the product of all prime numbers on the left, i.e. LCM(32, 80) by division method = 2 × 2 × 2 × 2 × 2 × 5 = 160.

☛ Also Check:

LCM of 32 and 80 Examples

Example 1: The GCD and LCM of two numbers are 16 and 160 respectively. If one number is 32, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 32 × m
⇒ m = (GCD × LCM)/32
⇒ m = (16 × 160)/32
⇒ m = 80
Therefore, the other number is 80.
Example 2: Verify the relationship between GCF and LCM of 32 and 80.

Solution:

The relation between GCF and LCM of 32 and 80 is given as,
LCM(32, 80) × GCF(32, 80) = Product of 32, 80
Prime factorization of 32 and 80 is given as, 32 = (2 × 2 × 2 × 2 × 2) = 2⁵ and 80 = (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹
LCM(32, 80) = 160
GCF(32, 80) = 16
LHS = LCM(32, 80) × GCF(32, 80) = 160 × 16 = 2560
RHS = Product of 32, 80 = 32 × 80 = 2560
⇒ LHS = RHS = 2560
Hence, verified.
Example 3: The product of two numbers is 2560. If their GCD is 16, what is their LCM?

Solution:

Given: GCD = 16
product of numbers = 2560
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2560/16
Therefore, the LCM is 160.
The probable combination for the given case is LCM(32, 80) = 160.

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FAQs on LCM of 32 and 80

What is the LCM of 32 and 80?

The LCM of 32 and 80 is 160. To find the least common multiple (LCM) of 32 and 80, we need to find the multiples of 32 and 80 (multiples of 32 = 32, 64, 96, 128 . . . . 160; multiples of 80 = 80, 160, 240, 320) and choose the smallest multiple that is exactly divisible by 32 and 80, i.e., 160.

If the LCM of 80 and 32 is 160, Find its GCF.

LCM(80, 32) × GCF(80, 32) = 80 × 32
Since the LCM of 80 and 32 = 160
⇒ 160 × GCF(80, 32) = 2560
Therefore, the GCF (greatest common factor) = 2560/160 = 16.

What is the Least Perfect Square Divisible by 32 and 80?

The least number divisible by 32 and 80 = LCM(32, 80)
LCM of 32 and 80 = 2 × 2 × 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 32 and 80 = LCM(32, 80) × 2 × 5 = 1600 [Square root of 1600 = √1600 = ±40]
Therefore, 1600 is the required number.

Which of the following is the LCM of 32 and 80? 10, 25, 18, 160

The value of LCM of 32, 80 is the smallest common multiple of 32 and 80. The number satisfying the given condition is 160.

What is the Relation Between GCF and LCM of 32, 80?

The following equation can be used to express the relation between GCF and LCM of 32 and 80, i.e. GCF × LCM = 32 × 80.

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