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LCM of 120 and 144

LCM of 120 and 144 is the smallest number among all common multiples of 120 and 144. The first few multiples of 120 and 144 are (120, 240, 360, 480, . . . ) and (144, 288, 432, 576, 720, . . . ) respectively. There are 3 commonly used methods to find LCM of 120 and 144 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 120 and 144
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 120 and 144?

Answer: LCM of 120 and 144 is 720.

Explanation:

The LCM of two non-zero integers, x(120) and y(144), is the smallest positive integer m(720) that is divisible by both x(120) and y(144) without any remainder.

Methods to Find LCM of 120 and 144

The methods to find the LCM of 120 and 144 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 120 and 144 by Listing Multiples

To calculate the LCM of 120 and 144 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 120 (120, 240, 360, 480, . . . ) and 144 (144, 288, 432, 576, 720, . . . . )
Step 2: The common multiples from the multiples of 120 and 144 are 720, 1440, . . .
Step 3: The smallest common multiple of 120 and 144 is 720.

∴ The least common multiple of 120 and 144 = 720.

LCM of 120 and 144 by Division Method

To calculate the LCM of 120 and 144 by the division method, we will divide the numbers(120, 144) by their prime factors (preferably common). The product of these divisors gives the LCM of 120 and 144.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 120 and 144. Write this prime number(2) on the left of the given numbers(120 and 144), separated as per the ladder arrangement.
Step 2: If any of the given numbers (120, 144) 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 120 and 144 is the product of all prime numbers on the left, i.e. LCM(120, 144) by division method = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720.

LCM of 120 and 144 by Prime Factorization

Prime factorization of 120 and 144 is (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and (2 × 2 × 2 × 2 × 3 × 3) = 2⁴ × 3² respectively. LCM of 120 and 144 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3² × 5¹ = 720.
Hence, the LCM of 120 and 144 by prime factorization is 720.

☛ Also Check:

LCM of 120 and 144 Examples

Example 1: The product of two numbers is 17280. If their GCD is 24, what is their LCM?

Solution:

Given: GCD = 24
product of numbers = 17280
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 17280/24
Therefore, the LCM is 720.
The probable combination for the given case is LCM(120, 144) = 720.
Example 2: Verify the relationship between GCF and LCM of 120 and 144.

Solution:

The relation between GCF and LCM of 120 and 144 is given as,
LCM(120, 144) × GCF(120, 144) = Product of 120, 144
Prime factorization of 120 and 144 is given as, 120 = (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and 144 = (2 × 2 × 2 × 2 × 3 × 3) = 2⁴ × 3²
LCM(120, 144) = 720
GCF(120, 144) = 24
LHS = LCM(120, 144) × GCF(120, 144) = 720 × 24 = 17280
RHS = Product of 120, 144 = 120 × 144 = 17280
⇒ LHS = RHS = 17280
Hence, verified.
Example 3: The GCD and LCM of two numbers are 24 and 720 respectively. If one number is 120, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 120 × a
⇒ a = (GCD × LCM)/120
⇒ a = (24 × 720)/120
⇒ a = 144
Therefore, the other number is 144.

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FAQs on LCM of 120 and 144

What is the LCM of 120 and 144?

The LCM of 120 and 144 is 720. To find the LCM (least common multiple) of 120 and 144, we need to find the multiples of 120 and 144 (multiples of 120 = 120, 240, 360, 480 . . . . 720; multiples of 144 = 144, 288, 432, 576 . . . . 720) and choose the smallest multiple that is exactly divisible by 120 and 144, i.e., 720.

What is the Least Perfect Square Divisible by 120 and 144?

The least number divisible by 120 and 144 = LCM(120, 144)
LCM of 120 and 144 = 2 × 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 120 and 144 = LCM(120, 144) × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

How to Find the LCM of 120 and 144 by Prime Factorization?

To find the LCM of 120 and 144 using prime factorization, we will find the prime factors, (120 = 2 × 2 × 2 × 3 × 5) and (144 = 2 × 2 × 2 × 2 × 3 × 3). LCM of 120 and 144 is the product of prime factors raised to their respective highest exponent among the numbers 120 and 144.
⇒ LCM of 120, 144 = 2⁴ × 3² × 5¹ = 720.

If the LCM of 144 and 120 is 720, Find its GCF.

LCM(144, 120) × GCF(144, 120) = 144 × 120
Since the LCM of 144 and 120 = 720
⇒ 720 × GCF(144, 120) = 17280
Therefore, the GCF = 17280/720 = 24.

Which of the following is the LCM of 120 and 144? 24, 30, 720, 10

The value of LCM of 120, 144 is the smallest common multiple of 120 and 144. The number satisfying the given condition is 720.

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