Architecture

# What Is The Least Common Multiple Of 24 And 30, Least Common Multiple

LCM of 24 and 30 is the smallest number among all common multiples of 24 and 30. The first few multiples of 24 and 30 are (24, 48, 72, 96, 120, . . . ) and (30, 60, 90, 120, 150, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 30 – by prime factorization, by listing multiples, and by division method.

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 1 LCM of 24 and 30 2 List of Methods 3 Solved Examples 4 FAQs

Answer: LCM of 24 and 30 is 120.

Explanation:

The LCM of two non-zero integers, x(24) and y(30), is the smallest positive integer m(120) that is divisible by both x(24) and y(30) without any remainder.

Let's look at the different methods for finding the LCM of 24 and 30.

By Division MethodBy Listing MultiplesBy Prime Factorization Method

### LCM of 24 and 30 by Division Method

To calculate the LCM of 24 and 30 by the division method, we will divide the numbers(24, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 30.

Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 24 and 30 is the product of all prime numbers on the left, i.e. LCM(24, 30) by division method = 2 × 2 × 2 × 3 × 5 = 120.

### LCM of 24 and 30 by Listing Multiples

To calculate the LCM of 24 and 30 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 24 (24, 48, 72, 96, 120, . . . ) and 30 (30, 60, 90, 120, 150, 180, . . . . )Step 2: The common multiples from the multiples of 24 and 30 are 120, 240, . . .Step 3: The smallest common multiple of 24 and 30 is 120.

∴ The least common multiple of 24 and 30 = 120.

### LCM of 24 and 30 by Prime Factorization

Prime factorization of 24 and 30 is (2 × 2 × 2 × 3) = 23 × 31 and (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM of 24 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 × 51 = 120.Hence, the LCM of 24 and 30 by prime factorization is 120.

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## FAQs on LCM of 24 and 30

### What is the LCM of 24 and 30?

The LCM of 24 and 30 is 120. To find the least common multiple (LCM) of 24 and 30, we need to find the multiples of 24 and 30 (multiples of 24 = 24, 48, 72, 96 . . . . 120; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 24 and 30, i.e., 120.

### If the LCM of 30 and 24 is 120, Find its GCF.

LCM(30, 24) × GCF(30, 24) = 30 × 24Since the LCM of 30 and 24 = 120⇒ 120 × GCF(30, 24) = 720Therefore, the GCF = 720/120 = 6.

### What are the Methods to Find LCM of 24 and 30?

The commonly used methods to find the LCM of 24 and 30 are:

Prime Factorization MethodListing MultiplesDivision Method

### How to Find the LCM of 24 and 30 by Prime Factorization?

To find the LCM of 24 and 30 using prime factorization, we will find the prime factors, (24 = 2 × 2 × 2 × 3) and (30 = 2 × 3 × 5). LCM of 24 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 24 and 30.⇒ LCM of 24, 30 = 23 × 31 × 51 = 120.

### What is the Relation Between GCF and LCM of 24, 30?

The following equation can be used to express the relation between GCF and LCM of 24 and 30, i.e. GCF × LCM = 24 × 30.