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LCM of 32 and 60

LCM of 32 and 60 is the smallest number among all common multiples of 32 and 60. The first few multiples of 32 and 60 are (32, 64, 96, 128, . . . ) and (60, 120, 180, 240, 300, 360, 420, . . . ) respectively. There are 3 commonly used methods to find LCM of 32 and 60 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 32 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 32 and 60?

Answer: LCM of 32 and 60 is 480.

Explanation:

The LCM of two non-zero integers, x(32) and y(60), is the smallest positive integer m(480) that is divisible by both x(32) and y(60) without any remainder.

Methods to Find LCM of 32 and 60

The methods to find the LCM of 32 and 60 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 32 and 60 by Prime Factorization

Prime factorization of 32 and 60 is (2 × 2 × 2 × 2 × 2) = 2⁵ and (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ respectively. LCM of 32 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 3¹ × 5¹ = 480.
Hence, the LCM of 32 and 60 by prime factorization is 480.

LCM of 32 and 60 by Listing Multiples

To calculate the LCM of 32 and 60 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, . . . ) and 60 (60, 120, 180, 240, 300, 360, 420, . . . . )
Step 2: The common multiples from the multiples of 32 and 60 are 480, 960, . . .
Step 3: The smallest common multiple of 32 and 60 is 480.

∴ The least common multiple of 32 and 60 = 480.

LCM of 32 and 60 by Division Method

To calculate the LCM of 32 and 60 by the division method, we will divide the numbers(32, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 32 and 60.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 32 and 60. Write this prime number(2) on the left of the given numbers(32 and 60), separated as per the ladder arrangement.
Step 2: If any of the given numbers (32, 60) 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 60 is the product of all prime numbers on the left, i.e. LCM(32, 60) by division method = 2 × 2 × 2 × 2 × 2 × 3 × 5 = 480.

☛ Also Check:

LCM of 32 and 60 Examples

Example 1: Verify the relationship between GCF and LCM of 32 and 60.

Solution:

The relation between GCF and LCM of 32 and 60 is given as,
LCM(32, 60) × GCF(32, 60) = Product of 32, 60
Prime factorization of 32 and 60 is given as, 32 = (2 × 2 × 2 × 2 × 2) = 2⁵ and 60 = (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹
LCM(32, 60) = 480
GCF(32, 60) = 4
LHS = LCM(32, 60) × GCF(32, 60) = 480 × 4 = 1920
RHS = Product of 32, 60 = 32 × 60 = 1920
⇒ LHS = RHS = 1920
Hence, verified.
Example 2: The GCD and LCM of two numbers are 4 and 480 respectively. If one number is 60, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 60 × y
⇒ y = (GCD × LCM)/60
⇒ y = (4 × 480)/60
⇒ y = 32
Therefore, the other number is 32.
Example 3: The product of two numbers is 1920. If their GCD is 4, what is their LCM?

Solution:

Given: GCD = 4
product of numbers = 1920
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1920/4
Therefore, the LCM is 480.
The probable combination for the given case is LCM(32, 60) = 480.

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FAQs on LCM of 32 and 60

What is the LCM of 32 and 60?

The LCM of 32 and 60 is 480. To find the least common multiple (LCM) of 32 and 60, we need to find the multiples of 32 and 60 (multiples of 32 = 32, 64, 96, 128 . . . . 480; multiples of 60 = 60, 120, 180, 240 . . . . 480) and choose the smallest multiple that is exactly divisible by 32 and 60, i.e., 480.

What is the Least Perfect Square Divisible by 32 and 60?

The least number divisible by 32 and 60 = LCM(32, 60)
LCM of 32 and 60 = 2 × 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 32 and 60 = LCM(32, 60) × 2 × 3 × 5 = 14400 [Square root of 14400 = √14400 = ±120]
Therefore, 14400 is the required number.

What is the Relation Between GCF and LCM of 32, 60?

The following equation can be used to express the relation between GCF and LCM of 32 and 60, i.e. GCF × LCM = 32 × 60.

Which of the following is the LCM of 32 and 60? 5, 11, 42, 480

The value of LCM of 32, 60 is the smallest common multiple of 32 and 60. The number satisfying the given condition is 480.

If the LCM of 60 and 32 is 480, Find its GCF.

LCM(60, 32) × GCF(60, 32) = 60 × 32
Since the LCM of 60 and 32 = 480
⇒ 480 × GCF(60, 32) = 1920
Therefore, the greatest common factor (GCF) = 1920/480 = 4.

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