LCM of 7 and 24

LCM of 7 and 24 is the smallest number among all common multiples of 7 and 24. The first few multiples of 7 and 24 are (7, 14, 21, 28, 35, 42, . . . ) and (24, 48, 72, 96, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 24 - by prime factorization, by listing multiples, and by division method.

1.	LCM of 7 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 7 and 24?

Answer: LCM of 7 and 24 is 168.

Explanation:

The LCM of two non-zero integers, x(7) and y(24), is the smallest positive integer m(168) that is divisible by both x(7) and y(24) without any remainder.

Methods to Find LCM of 7 and 24

Let's look at the different methods for finding the LCM of 7 and 24.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 7 and 24 by Prime Factorization

Prime factorization of 7 and 24 is (7) = 7¹ and (2 × 2 × 2 × 3) = 2³ × 3¹ respectively. LCM of 7 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 7¹ = 168.
Hence, the LCM of 7 and 24 by prime factorization is 168.

LCM of 7 and 24 by Listing Multiples

To calculate the LCM of 7 and 24 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, 42, . . . ) and 24 (24, 48, 72, 96, 120, . . . . )
Step 2: The common multiples from the multiples of 7 and 24 are 168, 336, . . .
Step 3: The smallest common multiple of 7 and 24 is 168.

∴ The least common multiple of 7 and 24 = 168.

LCM of 7 and 24 by Division Method

To calculate the LCM of 7 and 24 by the division method, we will divide the numbers(7, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 24.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 24. Write this prime number(2) on the left of the given numbers(7 and 24), separated as per the ladder arrangement.
Step 2: If any of the given numbers (7, 24) 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 7 and 24 is the product of all prime numbers on the left, i.e. LCM(7, 24) by division method = 2 × 2 × 2 × 3 × 7 = 168.

☛ Also Check:

LCM of 7 and 24 Examples

Example 1: Verify the relationship between GCF and LCM of 7 and 24.

Solution:

The relation between GCF and LCM of 7 and 24 is given as,
LCM(7, 24) × GCF(7, 24) = Product of 7, 24
Prime factorization of 7 and 24 is given as, 7 = (7) = 7¹ and 24 = (2 × 2 × 2 × 3) = 2³ × 3¹
LCM(7, 24) = 168
GCF(7, 24) = 1
LHS = LCM(7, 24) × GCF(7, 24) = 168 × 1 = 168
RHS = Product of 7, 24 = 7 × 24 = 168
⇒ LHS = RHS = 168
Hence, verified.
Example 2: The GCD and LCM of two numbers are 1 and 168 respectively. If one number is 7, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 7 × b
⇒ b = (GCD × LCM)/7
⇒ b = (1 × 168)/7
⇒ b = 24
Therefore, the other number is 24.
Example 3: The product of two numbers is 168. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 168
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 168/1
Therefore, the LCM is 168.
The probable combination for the given case is LCM(7, 24) = 168.

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FAQs on LCM of 7 and 24

What is the LCM of 7 and 24?

The LCM of 7 and 24 is 168. To find the least common multiple of 7 and 24, we need to find the multiples of 7 and 24 (multiples of 7 = 7, 14, 21, 28 . . . . 168; multiples of 24 = 24, 48, 72, 96 . . . . 168) and choose the smallest multiple that is exactly divisible by 7 and 24, i.e., 168.

What are the Methods to Find LCM of 7 and 24?

The commonly used methods to find the LCM of 7 and 24 are:

Division Method
Listing Multiples
Prime Factorization Method

If the LCM of 24 and 7 is 168, Find its GCF.

LCM(24, 7) × GCF(24, 7) = 24 × 7
Since the LCM of 24 and 7 = 168
⇒ 168 × GCF(24, 7) = 168
Therefore, the greatest common factor (GCF) = 168/168 = 1.

How to Find the LCM of 7 and 24 by Prime Factorization?

To find the LCM of 7 and 24 using prime factorization, we will find the prime factors, (7 = 7) and (24 = 2 × 2 × 2 × 3). LCM of 7 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 24.
⇒ LCM of 7, 24 = 2³ × 3¹ × 7¹ = 168.

Which of the following is the LCM of 7 and 24? 50, 168, 35, 24

The value of LCM of 7, 24 is the smallest common multiple of 7 and 24. The number satisfying the given condition is 168.

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