LCM of 12 and 30

LCM of 12 and 30 is the smallest number among all common multiples of 12 and 30. The first few multiples of 12 and 30 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (30, 60, 90, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 30 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 12 and 30 is 60.

Explanation:

The LCM of two non-zero integers, x(12) and y(30), is the smallest positive integer m(60) that is divisible by both x(12) and y(30) without any remainder.

Let's look at the different methods for finding the LCM of 12 and 30.

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

LCM of 12 and 30 by Prime Factorization

Prime factorization of 12 and 30 is (2 × 2 × 3) = 2² × 3¹ and (2 × 3 × 5) = 2¹ × 3¹ × 5¹ respectively. LCM of 12 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 12 and 30 by prime factorization is 60.

LCM of 12 and 30 by Listing Multiples

To calculate the LCM of 12 and 30 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, 72, 84, . . . ) and 30 (30, 60, 90, 120, . . . . )
• Step 2: The common multiples from the multiples of 12 and 30 are 60, 120, . . .
• Step 3: The smallest common multiple of 12 and 30 is 60.

∴ The least common multiple of 12 and 30 = 60.

LCM of 12 and 30 by Division Method

To calculate the LCM of 12 and 30 by the division method, we will divide the numbers(12, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 30.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 30. Write this prime number(2) on the left of the given numbers(12 and 30), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 30) 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 30 is the product of all prime numbers on the left, i.e. LCM(12, 30) by division method = 2 × 2 × 3 × 5 = 60.

☛ Also Check:

• LCM of 11 and 15 - 165
• LCM of 11 and 13 - 143
• LCM of 11 and 121 - 121
• LCM of 11 and 12 - 132
• LCM of 108 and 144 - 432
• LCM of 105 and 195 - 1365
• LCM of 100 and 200 - 200

FAQs on LCM of 12 and 30

What is the LCM of 12 and 30?

The LCM of 12 and 30 is 60. To find the LCM of 12 and 30, we need to find the multiples of 12 and 30 (multiples of 12 = 12, 24, 36, 48 . . . . 60; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 12 and 30, i.e., 60.

What is the Least Perfect Square Divisible by 12 and 30?

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

What is the Relation Between GCF and LCM of 12, 30?

The following equation can be used to express the relation between GCF and LCM of 12 and 30, i.e. GCF × LCM = 12 × 30.

How to Find the LCM of 12 and 30 by Prime Factorization?

To find the LCM of 12 and 30 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (30 = 2 × 3 × 5). LCM of 12 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 30.
⇒ LCM of 12, 30 = 2² × 3¹ × 5¹ = 60.

If the LCM of 30 and 12 is 60, Find its GCF.

LCM(30, 12) × GCF(30, 12) = 30 × 12
Since the LCM of 30 and 12 = 60
⇒ 60 × GCF(30, 12) = 360
Therefore, the greatest common factor (GCF) = 360/60 = 6.