LCM the 24 and 32 is the the smallest number among all typical multiples that 24 and 32. The first couple of multiples that 24 and 32 room (24, 48, 72, 96, 120, 144, 168, . . . ) and also (32, 64, 96, 128, 160, . . . ) respectively. There space 3 generally used techniques to uncover LCM of 24 and also 32 - by prime factorization, through listing multiples, and also by department method.

You are watching: What is the lcm of 24 and 32

1. | LCM that 24 and 32 |

2. | List that Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM the 24 and 32 is 96.

**Explanation: **

The LCM of two non-zero integers, x(24) and also y(32), is the smallest hopeful integer m(96) the is divisible through both x(24) and y(32) without any type of remainder.

The approaches to discover the LCM that 24 and 32 are defined below.

By prime Factorization MethodBy department MethodBy Listing Multiples### LCM of 24 and 32 by prime Factorization

Prime administrate of 24 and 32 is (2 × 2 × 2 × 3) = 23 × 31 and (2 × 2 × 2 × 2 × 2) = 25 respectively. LCM of 24 and 32 have the right to be obtained by multiply prime components raised to their respective greatest power, i.e. 25 × 31 = 96.Hence, the LCM of 24 and also 32 by prime factorization is 96.

### LCM the 24 and also 32 by department Method

To calculation the LCM that 24 and also 32 through the department method, we will certainly divide the numbers(24, 32) by your prime components (preferably common). The product of these divisors offers the LCM the 24 and 32.

**Step 3:**continue the measures until just 1s are left in the last row.

The LCM that 24 and also 32 is the product of every prime number on the left, i.e. LCM(24, 32) by division method = 2 × 2 × 2 × 2 × 2 × 3 = 96.

### LCM the 24 and 32 by Listing Multiples

To calculate the LCM that 24 and 32 by listing the end the usual multiples, we deserve to follow the given below steps:

**Step 1:**list a few multiples of 24 (24, 48, 72, 96, 120, 144, 168, . . . ) and also 32 (32, 64, 96, 128, 160, . . . . )

**Step 2:**The common multiples from the multiples of 24 and 32 room 96, 192, . . .

**Step 3:**The smallest typical multiple of 24 and 32 is 96.

∴ The least common multiple of 24 and 32 = 96.

**☛ also Check:**

**Example 1: Verify the relationship in between GCF and also LCM the 24 and 32. **

**Solution: **

The relation between GCF and also LCM that 24 and also 32 is provided as,LCM(24, 32) × GCF(24, 32) = Product that 24, 32Prime administer of 24 and also 32 is offered as, 24 = (2 × 2 × 2 × 3) = 23 × 31 and 32 = (2 × 2 × 2 × 2 × 2) = 25LCM(24, 32) = 96GCF(24, 32) = 8LHS = LCM(24, 32) × GCF(24, 32) = 96 × 8 = 768RHS = Product that 24, 32 = 24 × 32 = 768⇒ LHS = RHS = 768Hence, verified.

**Example 2: The product of two numbers is 768. If your GCD is 8, what is your LCM? **

**Solution:**

Given: GCD = 8product of numbers = 768∵ LCM × GCD = product the numbers⇒ LCM = Product/GCD = 768/8Therefore, the LCM is 96.The probable combination for the given situation is LCM(24, 32) = 96.

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## FAQs ~ above LCM that 24 and also 32

### What is the LCM the 24 and also 32?

The **LCM the 24 and 32 is 96**. To discover the LCM (least typical multiple) of 24 and also 32, we need to discover the multiples that 24 and 32 (multiples that 24 = 24, 48, 72, 96; multiples the 32 = 32, 64, 96, 128) and also choose the the smallest multiple the is specifically divisible through 24 and also 32, i.e., 96.

### What is the least Perfect Square Divisible by 24 and also 32?

The least number divisible by 24 and 32 = LCM(24, 32)LCM of 24 and 32 = 2 × 2 × 2 × 2 × 2 × 3

### What is the Relation between GCF and also LCM that 24, 32?

The following equation have the right to be supplied to express the relation in between GCF and also LCM of 24 and 32, i.e. GCF × LCM = 24 × 32.

### If the LCM that 32 and 24 is 96, find its GCF.

LCM(32, 24) × GCF(32, 24) = 32 × 24Since the LCM the 32 and 24 = 96⇒ 96 × GCF(32, 24) = 768Therefore, the greatest common factor (GCF) = 768/96 = 8.

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### How to uncover the LCM of 24 and 32 by element Factorization?

To uncover the LCM of 24 and 32 using prime factorization, we will uncover the prime factors, (24 = 2 × 2 × 2 × 3) and also (32 = 2 × 2 × 2 × 2 × 2). LCM that 24 and 32 is the product the prime factors raised to your respective greatest exponent amongst the numbers 24 and also 32.⇒ LCM of 24, 32 = 25 × 31 = 96.