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LCM of 120 and 160

LCM of 120 and 160 is the smallest number among all common multiples of 120 and 160. The first few multiples of 120 and 160 are (120, 240, 360, 480, 600, 720, . . . ) and (160, 320, 480, 640, 800, 960, . . . ) respectively. There are 3 commonly used methods to find LCM of 120 and 160 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 120 and 160
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 120 and 160?

Answer: LCM of 120 and 160 is 480.

Explanation:

The LCM of two non-zero integers, x(120) and y(160), is the smallest positive integer m(480) that is divisible by both x(120) and y(160) without any remainder.

Methods to Find LCM of 120 and 160

The methods to find the LCM of 120 and 160 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 120 and 160 by Listing Multiples

To calculate the LCM of 120 and 160 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, 600, 720, . . . ) and 160 (160, 320, 480, 640, 800, 960, . . . . )
Step 2: The common multiples from the multiples of 120 and 160 are 480, 960, . . .
Step 3: The smallest common multiple of 120 and 160 is 480.

∴ The least common multiple of 120 and 160 = 480.

LCM of 120 and 160 by Division Method

To calculate the LCM of 120 and 160 by the division method, we will divide the numbers(120, 160) by their prime factors (preferably common). The product of these divisors gives the LCM of 120 and 160.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 120 and 160. Write this prime number(2) on the left of the given numbers(120 and 160), separated as per the ladder arrangement.
Step 2: If any of the given numbers (120, 160) 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 160 is the product of all prime numbers on the left, i.e. LCM(120, 160) by division method = 2 × 2 × 2 × 2 × 2 × 3 × 5 = 480.

LCM of 120 and 160 by Prime Factorization

Prime factorization of 120 and 160 is (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and (2 × 2 × 2 × 2 × 2 × 5) = 2⁵ × 5¹ respectively. LCM of 120 and 160 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 3¹ × 5¹ = 480.
Hence, the LCM of 120 and 160 by prime factorization is 480.

☛ Also Check:

LCM of 120 and 160 Examples

Example 1: The GCD and LCM of two numbers are 40 and 480 respectively. If one number is 120, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 120 × p
⇒ p = (GCD × LCM)/120
⇒ p = (40 × 480)/120
⇒ p = 160
Therefore, the other number is 160.
Example 2: Verify the relationship between GCF and LCM of 120 and 160.

Solution:

The relation between GCF and LCM of 120 and 160 is given as,
LCM(120, 160) × GCF(120, 160) = Product of 120, 160
Prime factorization of 120 and 160 is given as, 120 = (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and 160 = (2 × 2 × 2 × 2 × 2 × 5) = 2⁵ × 5¹
LCM(120, 160) = 480
GCF(120, 160) = 40
LHS = LCM(120, 160) × GCF(120, 160) = 480 × 40 = 19200
RHS = Product of 120, 160 = 120 × 160 = 19200
⇒ LHS = RHS = 19200
Hence, verified.
Example 3: The product of two numbers is 19200. If their GCD is 40, what is their LCM?

Solution:

Given: GCD = 40
product of numbers = 19200
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 19200/40
Therefore, the LCM is 480.
The probable combination for the given case is LCM(120, 160) = 480.

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FAQs on LCM of 120 and 160

What is the LCM of 120 and 160?

The LCM of 120 and 160 is 480. To find the least common multiple of 120 and 160, we need to find the multiples of 120 and 160 (multiples of 120 = 120, 240, 360, 480; multiples of 160 = 160, 320, 480, 640) and choose the smallest multiple that is exactly divisible by 120 and 160, i.e., 480.

What is the Relation Between GCF and LCM of 120, 160?

The following equation can be used to express the relation between GCF and LCM of 120 and 160, i.e. GCF × LCM = 120 × 160.

What is the Least Perfect Square Divisible by 120 and 160?

The least number divisible by 120 and 160 = LCM(120, 160)
LCM of 120 and 160 = 2 × 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 120 and 160 = LCM(120, 160) × 2 × 3 × 5 = 14400 [Square root of 14400 = √14400 = ±120]
Therefore, 14400 is the required number.

How to Find the LCM of 120 and 160 by Prime Factorization?

To find the LCM of 120 and 160 using prime factorization, we will find the prime factors, (120 = 2 × 2 × 2 × 3 × 5) and (160 = 2 × 2 × 2 × 2 × 2 × 5). LCM of 120 and 160 is the product of prime factors raised to their respective highest exponent among the numbers 120 and 160.
⇒ LCM of 120, 160 = 2⁵ × 3¹ × 5¹ = 480.

If the LCM of 160 and 120 is 480, Find its GCF.

LCM(160, 120) × GCF(160, 120) = 160 × 120
Since the LCM of 160 and 120 = 480
⇒ 480 × GCF(160, 120) = 19200
Therefore, the greatest common factor = 19200/480 = 40.

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