LCM of 120 and 180

LCM of 120 and 180 is the smallest number among all common multiples of 120 and 180. The first few multiples of 120 and 180 are (120, 240, 360, 480, 600, . . . ) and (180, 360, 540, 720, 900, 1080, 1260, . . . ) respectively. There are 3 commonly used methods to find LCM of 120 and 180 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 120 and 180 is 360.

Explanation:

The LCM of two non-zero integers, x(120) and y(180), is the smallest positive integer m(360) that is divisible by both x(120) and y(180) without any remainder.

The methods to find the LCM of 120 and 180 are explained below.

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

LCM of 120 and 180 by Prime Factorization

Prime factorization of 120 and 180 is (2 × 2 × 2 × 3 × 5) = 2³ × 3¹ × 5¹ and (2 × 2 × 3 × 3 × 5) = 2² × 3² × 5¹ respectively. LCM of 120 and 180 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 180 by prime factorization is 360.

LCM of 120 and 180 by Division Method

To calculate the LCM of 120 and 180 by the division method, we will divide the numbers(120, 180) by their prime factors (preferably common). The product of these divisors gives the LCM of 120 and 180.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 120 and 180. Write this prime number(2) on the left of the given numbers(120 and 180), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (120, 180) 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 180 is the product of all prime numbers on the left, i.e. LCM(120, 180) by division method = 2 × 2 × 2 × 3 × 3 × 5 = 360.

LCM of 120 and 180 by Listing Multiples

To calculate the LCM of 120 and 180 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, . . . ) and 180 (180, 360, 540, 720, 900, 1080, 1260, . . . . )
• Step 2: The common multiples from the multiples of 120 and 180 are 360, 720, . . .
• Step 3: The smallest common multiple of 120 and 180 is 360.

∴ The least common multiple of 120 and 180 = 360.

☛ Also Check:

• LCM of 4, 10 and 12 - 60
• LCM of 378, 180 and 420 - 3780
• LCM of 36, 60 and 72 - 360
• LCM of 36, 54 and 72 - 216
• LCM of 36, 48 and 72 - 144
• LCM of 36, 48 and 54 - 432
• LCM of 36, 42 and 72 - 504

FAQs on LCM of 120 and 180

What is the LCM of 120 and 180?

The LCM of 120 and 180 is 360. To find the least common multiple (LCM) of 120 and 180, we need to find the multiples of 120 and 180 (multiples of 120 = 120, 240, 360, 480; multiples of 180 = 180, 360, 540, 720) and choose the smallest multiple that is exactly divisible by 120 and 180, i.e., 360.

If the LCM of 180 and 120 is 360, Find its GCF.

LCM(180, 120) × GCF(180, 120) = 180 × 120
Since the LCM of 180 and 120 = 360
⇒ 360 × GCF(180, 120) = 21600
Therefore, the GCF = 21600/360 = 60.

Which of the following is the LCM of 120 and 180? 360, 40, 10, 42

The value of LCM of 120, 180 is the smallest common multiple of 120 and 180. The number satisfying the given condition is 360.

How to Find the LCM of 120 and 180 by Prime Factorization?

To find the LCM of 120 and 180 using prime factorization, we will find the prime factors, (120 = 2 × 2 × 2 × 3 × 5) and (180 = 2 × 2 × 3 × 3 × 5). LCM of 120 and 180 is the product of prime factors raised to their respective highest exponent among the numbers 120 and 180.
⇒ LCM of 120, 180 = 2³ × 3² × 5¹ = 360.

What are the Methods to Find LCM of 120 and 180?

The commonly used methods to find the LCM of 120 and 180 are:

• Prime Factorization Method
• Listing Multiples
• Division Method