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LCM of 24, 40, 80, and 120

LCM of 24, 40, 80, and 120 is the smallest number among all common multiples of 24, 40, 80, and 120. The first few multiples of 24, 40, 80, and 120 are (24, 48, 72, 96, 120 . . .), (40, 80, 120, 160, 200 . . .), (80, 160, 240, 320, 400 . . .), and (120, 240, 360, 480, 600 . . .) respectively. There are 3 commonly used methods to find LCM of 24, 40, 80, 120 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 24, 40, 80, and 120
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 24, 40, 80, and 120?

Answer: LCM of 24, 40, 80, and 120 is 240.

Explanation:

The LCM of four non-zero integers, a(24), b(40), c(80), and d(120), is the smallest positive integer m(240) that is divisible by a(24), b(40), c(80), and d(120) without any remainder.

Methods to Find LCM of 24, 40, 80, and 120

The methods to find the LCM of 24, 40, 80, and 120 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 24, 40, 80, and 120 by Division Method

To calculate the LCM of 24, 40, 80, and 120 by the division method, we will divide the numbers(24, 40, 80, 120) by their prime factors (preferably common). The product of these divisors gives the LCM of 24, 40, 80, and 120.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24, 40, 80, and 120. Write this prime number(2) on the left of the given numbers(24, 40, 80, and 120), separated as per the ladder arrangement.
Step 2: If any of the given numbers (24, 40, 80, 120) 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 24, 40, 80, and 120 is the product of all prime numbers on the left, i.e. LCM(24, 40, 80, 120) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

LCM of 24, 40, 80, and 120 by Prime Factorization

Prime factorization of 24, 40, 80, and 120 is (2 × 2 × 2 × 3) = 2³ × 3¹, (2 × 2 × 2 × 5) = 2³ × 5¹, (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹, and (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ respectively. LCM of 24, 40, 80, and 120 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5¹ = 240.
Hence, the LCM of 24, 40, 80, and 120 by prime factorization is 240.

LCM of 24, 40, 80, and 120 by Listing Multiples

To calculate the LCM of 24, 40, 80, 120 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 . . .), 40 (40, 80, 120, 160, 200 . . .), 80 (80, 160, 240, 320, 400 . . .), and 120 (120, 240, 360, 480, 600 . . .).
Step 2: The common multiples from the multiples of 24, 40, 80, and 120 are 240, 480, . . .
Step 3: The smallest common multiple of 24, 40, 80, and 120 is 240.

∴ The least common multiple of 24, 40, 80, and 120 = 240.

☛ Also Check:

LCM of 24, 40, 80, and 120 Examples

Example 1: Find the smallest number that is divisible by 24, 40, 80, 120 exactly.

Solution:

The smallest number that is divisible by 24, 40, 80, and 120 exactly is their LCM.
⇒ Multiples of 24, 40, 80, and 120:
- Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, . . . .
- Multiples of 40 = 40, 80, 120, 160, 200, 240, . . . .
- Multiples of 80 = 80, 160, 240, 320, 400, . . . .
- Multiples of 120 = 120, 240, 360, 480, 600, . . . .
Therefore, the LCM of 24, 40, 80, and 120 is 240.
Example 2: Find the smallest number which when divided by 24, 40, 80, and 120 leaves 14 as the remainder in each case.

Solution:

The smallest number exactly divisible by 24, 40, 80, and 120 = LCM(24, 40, 80, 120) ⇒ Smallest number which leaves 14 as remainder when divided by 24, 40, 80, and 120 = LCM(24, 40, 80, 120) + 14
- 24 = 2³ × 3¹
- 40 = 2³ × 5¹
- 80 = 2⁴ × 5¹
- 120 = 2³ × 3¹ × 5¹
LCM(24, 40, 80, 120) = 2⁴ × 3¹ × 5¹ = 240
⇒ The required number = 240 + 14 = 254.
Example 3: Which of the following is the LCM of 24, 40, 80, 120? 24, 36, 240, 3.

Solution:

The value of LCM of 24, 40, 80, and 120 is the smallest common multiple of 24, 40, 80, and 120. The number satisfying the given condition is 240. ∴LCM(24, 40, 80, 120) = 240.

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FAQs on LCM of 24, 40, 80, and 120

What is the LCM of 24, 40, 80, and 120?

The LCM of 24, 40, 80, and 120 is 240. To find the least common multiple (LCM) of 24, 40, 80, and 120, we need to find the multiples of 24, 40, 80, and 120 (multiples of 24 = 24, 48, 72, 96 . . . . 240 . . . . ; multiples of 40 = 40, 80, 120, 160, 240 . . . .; multiples of 80 = 80, 160, 240, 320 . . . .; multiples of 120 = 120, 240, 360, 480 . . . .) and choose the smallest multiple that is exactly divisible by 24, 40, 80, and 120, i.e., 240.

Which of the following is the LCM of 24, 40, 80, and 120? 52, 240, 2, 3

The value of LCM of 24, 40, 80, 120 is the smallest common multiple of 24, 40, 80, and 120. The number satisfying the given condition is 240.

What are the Methods to Find LCM of 24, 40, 80, 120?

The commonly used methods to find the LCM of 24, 40, 80, 120 are:

Listing Multiples
Division Method
Prime Factorization Method

What is the Least Perfect Square Divisible by 24, 40, 80, and 120?

The least number divisible by 24, 40, 80, and 120 = LCM(24, 40, 80, 120)
LCM of 24, 40, 80, and 120 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 24, 40, 80, and 120 = LCM(24, 40, 80, 120) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

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