LCM of 5 and 24

LCM of 5 and 24 is the smallest number among all common multiples of 5 and 24. The first few multiples of 5 and 24 are (5, 10, 15, 20, 25, 30, 35, . . . ) and (24, 48, 72, 96, 120, 144, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 24 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 5 and 24 is 120.

Explanation:

The LCM of two non-zero integers, x(5) and y(24), is the smallest positive integer m(120) that is divisible by both x(5) and y(24) without any remainder.

The methods to find the LCM of 5 and 24 are explained below.

• By Prime Factorization Method
• By Division Method
• By Listing Multiples

LCM of 5 and 24 by Prime Factorization

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

LCM of 5 and 24 by Division Method

To calculate the LCM of 5 and 24 by the division method, we will divide the numbers(5, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 24. Write this prime number(2) on the left of the given numbers(5 and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (5, 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 5 and 24 is the product of all prime numbers on the left, i.e. LCM(5, 24) by division method = 2 × 2 × 2 × 3 × 5 = 120.

LCM of 5 and 24 by Listing Multiples

To calculate the LCM of 5 and 24 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, 35, . . . ) and 24 (24, 48, 72, 96, 120, 144, 168, . . . . )
• Step 2: The common multiples from the multiples of 5 and 24 are 120, 240, . . .
• Step 3: The smallest common multiple of 5 and 24 is 120.

∴ The least common multiple of 5 and 24 = 120.

☛ Also Check:

• LCM of 9 and 24 - 72
• LCM of 6 and 14 - 42
• LCM of 10 and 24 - 120
• LCM of 5 and 7 - 35
• LCM of 42 and 70 - 210
• LCM of 30 and 54 - 270
• LCM of 8, 9 and 10 - 360

FAQs on LCM of 5 and 24

What is the LCM of 5 and 24?

The LCM of 5 and 24 is 120. To find the least common multiple (LCM) of 5 and 24, we need to find the multiples of 5 and 24 (multiples of 5 = 5, 10, 15, 20 . . . . 120; multiples of 24 = 24, 48, 72, 96 . . . . 120) and choose the smallest multiple that is exactly divisible by 5 and 24, i.e., 120.

Which of the following is the LCM of 5 and 24? 120, 20, 36, 45

The value of LCM of 5, 24 is the smallest common multiple of 5 and 24. The number satisfying the given condition is 120.

What are the Methods to Find LCM of 5 and 24?

The commonly used methods to find the LCM of 5 and 24 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

How to Find the LCM of 5 and 24 by Prime Factorization?

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

If the LCM of 24 and 5 is 120, Find its GCF.

LCM(24, 5) × GCF(24, 5) = 24 × 5
Since the LCM of 24 and 5 = 120
⇒ 120 × GCF(24, 5) = 120
Therefore, the greatest common factor (GCF) = 120/120 = 1.