LCM of 4, 12, 16, and 24

LCM of 4, 12, 16, and 24 is the smallest number among all common multiples of 4, 12, 16, and 24. The first few multiples of 4, 12, 16, and 24 are (4, 8, 12, 16, 20 . . .), (12, 24, 36, 48, 60 . . .), (16, 32, 48, 64, 80 . . .), and (24, 48, 72, 96, 120 . . .) respectively. There are 3 commonly used methods to find LCM of 4, 12, 16, 24 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 4, 12, 16, and 24 is 48.

Explanation:

The LCM of four non-zero integers, a(4), b(12), c(16), and d(24), is the smallest positive integer m(48) that is divisible by a(4), b(12), c(16), and d(24) without any remainder.

The methods to find the LCM of 4, 12, 16, and 24 are explained below.

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

LCM of 4, 12, 16, and 24 by Listing Multiples

To calculate the LCM of 4, 12, 16, 24 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 4 (4, 8, 12, 16, 20 . . .), 12 (12, 24, 36, 48, 60 . . .), 16 (16, 32, 48, 64, 80 . . .), and 24 (24, 48, 72, 96, 120 . . .).
• Step 2: The common multiples from the multiples of 4, 12, 16, and 24 are 48, 96, . . .
• Step 3: The smallest common multiple of 4, 12, 16, and 24 is 48.

∴ The least common multiple of 4, 12, 16, and 24 = 48.

LCM of 4, 12, 16, and 24 by Prime Factorization

Prime factorization of 4, 12, 16, and 24 is (2 × 2) = 2², (2 × 2 × 3) = 2² × 3¹, (2 × 2 × 2 × 2) = 2⁴, and (2 × 2 × 2 × 3) = 2³ × 3¹ respectively. LCM of 4, 12, 16, and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ = 48.
Hence, the LCM of 4, 12, 16, and 24 by prime factorization is 48.

LCM of 4, 12, 16, and 24 by Division Method

To calculate the LCM of 4, 12, 16, and 24 by the division method, we will divide the numbers(4, 12, 16, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 4, 12, 16, and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4, 12, 16, and 24. Write this prime number(2) on the left of the given numbers(4, 12, 16, and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 12, 16, 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 4, 12, 16, and 24 is the product of all prime numbers on the left, i.e. LCM(4, 12, 16, 24) by division method = 2 × 2 × 2 × 2 × 3 = 48.

☛ Also Check:

• LCM of 13 and 26 - 26
• LCM of 3 and 5 - 15
• LCM of 12 and 24 - 24
• LCM of 15, 25, 40 and 75 - 600
• LCM of 13 and 52 - 52
• LCM of 2923 and 3239 - 119843
• LCM of 24 and 54 - 216

FAQs on LCM of 4, 12, 16, and 24

What is the LCM of 4, 12, 16, and 24?

The LCM of 4, 12, 16, and 24 is 48. To find the LCM of 4, 12, 16, and 24, we need to find the multiples of 4, 12, 16, and 24 (multiples of 4 = 4, 8, 12, 16 . . . . 48 . . . . ; multiples of 12 = 12, 24, 36, 48 . . . .; multiples of 16 = 16, 32, 48, 64 . . . .; multiples of 24 = 24, 48, 72, 96 . . . .) and choose the smallest multiple that is exactly divisible by 4, 12, 16, and 24, i.e., 48.

Which of the following is the LCM of 4, 12, 16, and 24? 48, 32, 27, 100

The value of LCM of 4, 12, 16, 24 is the smallest common multiple of 4, 12, 16, and 24. The number satisfying the given condition is 48.

What are the Methods to Find LCM of 4, 12, 16, 24?

The commonly used methods to find the LCM of 4, 12, 16, 24 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Least Perfect Square Divisible by 4, 12, 16, and 24?

The least number divisible by 4, 12, 16, and 24 = LCM(4, 12, 16, 24)
LCM of 4, 12, 16, and 24 = 2 × 2 × 2 × 2 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 4, 12, 16, and 24 = LCM(4, 12, 16, 24) × 3 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.