LCM of 12 and 90

LCM of 12 and 90 is the smallest number among all common multiples of 12 and 90. The first few multiples of 12 and 90 are (12, 24, 36, 48, 60, . . . ) and (90, 180, 270, 360, 450, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 90 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 12 and 90 is 180.

Explanation:

The LCM of two non-zero integers, x(12) and y(90), is the smallest positive integer m(180) that is divisible by both x(12) and y(90) without any remainder.

Let's look at the different methods for finding the LCM of 12 and 90.

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

LCM of 12 and 90 by Listing Multiples

To calculate the LCM of 12 and 90 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, . . . ) and 90 (90, 180, 270, 360, 450, . . . . )
• Step 2: The common multiples from the multiples of 12 and 90 are 180, 360, . . .
• Step 3: The smallest common multiple of 12 and 90 is 180.

∴ The least common multiple of 12 and 90 = 180.

LCM of 12 and 90 by Prime Factorization

Prime factorization of 12 and 90 is (2 × 2 × 3) = 2² × 3¹ and (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ respectively. LCM of 12 and 90 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 5¹ = 180.
Hence, the LCM of 12 and 90 by prime factorization is 180.

LCM of 12 and 90 by Division Method

To calculate the LCM of 12 and 90 by the division method, we will divide the numbers(12, 90) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 90.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 90. Write this prime number(2) on the left of the given numbers(12 and 90), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 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 12 and 90 is the product of all prime numbers on the left, i.e. LCM(12, 90) by division method = 2 × 2 × 3 × 3 × 5 = 180.

☛ Also Check:

• LCM of 5, 6 and 9 - 90
• LCM of 5, 6 and 7 - 210
• LCM of 5, 6 and 10 - 30
• LCM of 5, 15 and 20 - 60
• LCM of 5, 10 and 15 - 30
• LCM of 48, 56 and 72 - 1008
• LCM of 45, 60 and 75 - 900

FAQs on LCM of 12 and 90

What is the LCM of 12 and 90?

The LCM of 12 and 90 is 180. To find the least common multiple (LCM) of 12 and 90, we need to find the multiples of 12 and 90 (multiples of 12 = 12, 24, 36, 48 . . . . 180; multiples of 90 = 90, 180, 270, 360) and choose the smallest multiple that is exactly divisible by 12 and 90, i.e., 180.

If the LCM of 90 and 12 is 180, Find its GCF.

LCM(90, 12) × GCF(90, 12) = 90 × 12
Since the LCM of 90 and 12 = 180
⇒ 180 × GCF(90, 12) = 1080
Therefore, the greatest common factor = 1080/180 = 6.

What are the Methods to Find LCM of 12 and 90?

The commonly used methods to find the LCM of 12 and 90 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

What is the Least Perfect Square Divisible by 12 and 90?

The least number divisible by 12 and 90 = LCM(12, 90)
LCM of 12 and 90 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 12 and 90 = LCM(12, 90) × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

How to Find the LCM of 12 and 90 by Prime Factorization?

To find the LCM of 12 and 90 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (90 = 2 × 3 × 3 × 5). LCM of 12 and 90 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 90.
⇒ LCM of 12, 90 = 2² × 3² × 5¹ = 180.