LCM of 3 and 24

LCM of 3 and 24 is the smallest number among all common multiples of 3 and 24. The first few multiples of 3 and 24 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (24, 48, 72, 96, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 24 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 3 and 24 is 24.

Explanation:

The LCM of two non-zero integers, x(3) and y(24), is the smallest positive integer m(24) that is divisible by both x(3) and y(24) without any remainder.

The methods to find the LCM of 3 and 24 are explained below.

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

LCM of 3 and 24 by Prime Factorization

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

LCM of 3 and 24 by Division Method

To calculate the LCM of 3 and 24 by the division method, we will divide the numbers(3, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 24.

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

LCM of 3 and 24 by Listing Multiples

To calculate the LCM of 3 and 24 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 24 (24, 48, 72, 96, . . . . )
• Step 2: The common multiples from the multiples of 3 and 24 are 24, 48, . . .
• Step 3: The smallest common multiple of 3 and 24 is 24.

∴ The least common multiple of 3 and 24 = 24.

☛ Also Check:

• LCM of 4, 7 and 14 - 28
• LCM of 56 and 84 - 168
• LCM of 4, 8 and 16 - 16
• LCM of 8 and 64 - 64
• LCM of 7 and 21 - 21
• LCM of 6, 9 and 12 - 36
• LCM of 12 and 40 - 120

FAQs on LCM of 3 and 24

What is the LCM of 3 and 24?

The LCM of 3 and 24 is 24. To find the least common multiple of 3 and 24, we need to find the multiples of 3 and 24 (multiples of 3 = 3, 6, 9, 12 . . . . 24; multiples of 24 = 24, 48, 72, 96) and choose the smallest multiple that is exactly divisible by 3 and 24, i.e., 24.

What is the Least Perfect Square Divisible by 3 and 24?

The least number divisible by 3 and 24 = LCM(3, 24)
LCM of 3 and 24 = 2 × 2 × 2 × 3 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 3 and 24 = LCM(3, 24) × 2 × 3 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

If the LCM of 24 and 3 is 24, Find its GCF.

LCM(24, 3) × GCF(24, 3) = 24 × 3
Since the LCM of 24 and 3 = 24
⇒ 24 × GCF(24, 3) = 72
Therefore, the GCF = 72/24 = 3.

Which of the following is the LCM of 3 and 24? 11, 20, 25, 24

The value of LCM of 3, 24 is the smallest common multiple of 3 and 24. The number satisfying the given condition is 24.

How to Find the LCM of 3 and 24 by Prime Factorization?

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