LCM of 12 and 45

LCM of 12 and 45 is the smallest number among all common multiples of 12 and 45. The first few multiples of 12 and 45 are (12, 24, 36, 48, . . . ) and (45, 90, 135, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 45 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 12 and 45 is 180.

Explanation:

The LCM of two non-zero integers, x(12) and y(45), is the smallest positive integer m(180) that is divisible by both x(12) and y(45) without any remainder.

Let's look at the different methods for finding the LCM of 12 and 45.

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

LCM of 12 and 45 by Division Method

To calculate the LCM of 12 and 45 by the division method, we will divide the numbers(12, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 45. Write this prime number(2) on the left of the given numbers(12 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 45) 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 45 is the product of all prime numbers on the left, i.e. LCM(12, 45) by division method = 2 × 2 × 3 × 3 × 5 = 180.

LCM of 12 and 45 by Prime Factorization

Prime factorization of 12 and 45 is (2 × 2 × 3) = 2² × 3¹ and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 12 and 45 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 45 by prime factorization is 180.

LCM of 12 and 45 by Listing Multiples

To calculate the LCM of 12 and 45 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, . . . ) and 45 (45, 90, 135, 180, . . . . )
• Step 2: The common multiples from the multiples of 12 and 45 are 180, 360, . . .
• Step 3: The smallest common multiple of 12 and 45 is 180.

∴ The least common multiple of 12 and 45 = 180.

☛ Also Check:

• LCM of 8, 16 and 24 - 48
• LCM of 8, 15 and 20 - 120
• LCM of 8, 15 and 21 - 840
• LCM of 8, 12 and 18 - 72
• LCM of 8, 12 and 16 - 48
• LCM of 8, 12 and 15 - 120
• LCM of 8, 12 and 20 - 120

FAQs on LCM of 12 and 45

What is the LCM of 12 and 45?

The LCM of 12 and 45 is 180. To find the least common multiple of 12 and 45, we need to find the multiples of 12 and 45 (multiples of 12 = 12, 24, 36, 48 . . . . 180; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 12 and 45, i.e., 180.

If the LCM of 45 and 12 is 180, Find its GCF.

LCM(45, 12) × GCF(45, 12) = 45 × 12
Since the LCM of 45 and 12 = 180
⇒ 180 × GCF(45, 12) = 540
Therefore, the GCF = 540/180 = 3.

What is the Relation Between GCF and LCM of 12, 45?

The following equation can be used to express the relation between GCF and LCM of 12 and 45, i.e. GCF × LCM = 12 × 45.

What is the Least Perfect Square Divisible by 12 and 45?

The least number divisible by 12 and 45 = LCM(12, 45)
LCM of 12 and 45 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 12 and 45 = LCM(12, 45) × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

Which of the following is the LCM of 12 and 45? 20, 30, 15, 180

The value of LCM of 12, 45 is the smallest common multiple of 12 and 45. The number satisfying the given condition is 180.