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LCM of 120 and 90

LCM of 120 and 90 is the smallest number among all common multiples of 120 and 90. The first few multiples of 120 and 90 are (120, 240, 360, 480, . . . ) and (90, 180, 270, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 120 and 90 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 120 and 90
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 120 and 90?

Answer: LCM of 120 and 90 is 360.

Explanation:

The LCM of two non-zero integers, x(120) and y(90), is the smallest positive integer m(360) that is divisible by both x(120) and y(90) without any remainder.

Methods to Find LCM of 120 and 90

The methods to find the LCM of 120 and 90 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 120 and 90 by Prime Factorization

Prime factorization of 120 and 90 is (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ respectively. LCM of 120 and 90 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² × 5¹ = 360.
Hence, the LCM of 120 and 90 by prime factorization is 360.

LCM of 120 and 90 by Listing Multiples

To calculate the LCM of 120 and 90 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 90 (90, 180, 270, 360, . . . . )
Step 2: The common multiples from the multiples of 120 and 90 are 360, 720, . . .
Step 3: The smallest common multiple of 120 and 90 is 360.

∴ The least common multiple of 120 and 90 = 360.

LCM of 120 and 90 by Division Method

To calculate the LCM of 120 and 90 by the division method, we will divide the numbers(120, 90) by their prime factors (preferably common). The product of these divisors gives the LCM of 120 and 90.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 120 and 90. Write this prime number(2) on the left of the given numbers(120 and 90), separated as per the ladder arrangement.
Step 2: If any of the given numbers (120, 90) 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 90 is the product of all prime numbers on the left, i.e. LCM(120, 90) by division method = 2 × 2 × 2 × 3 × 3 × 5 = 360.

☛ Also Check:

LCM of 120 and 90 Examples

Example 1: The product of two numbers is 10800. If their GCD is 30, what is their LCM?

Solution:

Given: GCD = 30
product of numbers = 10800
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 10800/30
Therefore, the LCM is 360.
The probable combination for the given case is LCM(120, 90) = 360.
Example 2: Verify the relationship between GCF and LCM of 120 and 90.

Solution:

The relation between GCF and LCM of 120 and 90 is given as,
LCM(120, 90) × GCF(120, 90) = Product of 120, 90
Prime factorization of 120 and 90 is given as, 120 = (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and 90 = (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹
LCM(120, 90) = 360
GCF(120, 90) = 30
LHS = LCM(120, 90) × GCF(120, 90) = 360 × 30 = 10800
RHS = Product of 120, 90 = 120 × 90 = 10800
⇒ LHS = RHS = 10800
Hence, verified.
Example 3: The GCD and LCM of two numbers are 30 and 360 respectively. If one number is 90, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 90 × y
⇒ y = (GCD × LCM)/90
⇒ y = (30 × 360)/90
⇒ y = 120
Therefore, the other number is 120.

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FAQs on LCM of 120 and 90

What is the LCM of 120 and 90?

The LCM of 120 and 90 is 360. To find the LCM (least common multiple) of 120 and 90, we need to find the multiples of 120 and 90 (multiples of 120 = 120, 240, 360, 480; multiples of 90 = 90, 180, 270, 360) and choose the smallest multiple that is exactly divisible by 120 and 90, i.e., 360.

What is the Least Perfect Square Divisible by 120 and 90?

The least number divisible by 120 and 90 = LCM(120, 90)
LCM of 120 and 90 = 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 120 and 90 = LCM(120, 90) × 2 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

What is the Relation Between GCF and LCM of 120, 90?

The following equation can be used to express the relation between GCF and LCM of 120 and 90, i.e. GCF × LCM = 120 × 90.

If the LCM of 90 and 120 is 360, Find its GCF.

LCM(90, 120) × GCF(90, 120) = 90 × 120
Since the LCM of 90 and 120 = 360
⇒ 360 × GCF(90, 120) = 10800
Therefore, the greatest common factor (GCF) = 10800/360 = 30.

Which of the following is the LCM of 120 and 90? 32, 360, 11, 50

The value of LCM of 120, 90 is the smallest common multiple of 120 and 90. The number satisfying the given condition is 360.

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