LCM of 3, 6, 9, and 12

LCM of 3, 6, 9, and 12 is the smallest number among all common multiples of 3, 6, 9, and 12. The first few multiples of 3, 6, 9, and 12 are (3, 6, 9, 12, 15 . . .), (6, 12, 18, 24, 30 . . .), (9, 18, 27, 36, 45 . . .), and (12, 24, 36, 48, 60 . . .) respectively. There are 3 commonly used methods to find LCM of 3, 6, 9, 12 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 3, 6, 9, and 12 is 36.

Explanation:

The LCM of four non-zero integers, a(3), b(6), c(9), and d(12), is the smallest positive integer m(36) that is divisible by a(3), b(6), c(9), and d(12) without any remainder.

The methods to find the LCM of 3, 6, 9, and 12 are explained below.

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

LCM of 3, 6, 9, and 12 by Division Method

To calculate the LCM of 3, 6, 9, and 12 by the division method, we will divide the numbers(3, 6, 9, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 3, 6, 9, and 12.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3, 6, 9, and 12. Write this prime number(2) on the left of the given numbers(3, 6, 9, and 12), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (3, 6, 9, 12) 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 3, 6, 9, and 12 is the product of all prime numbers on the left, i.e. LCM(3, 6, 9, 12) by division method = 2 × 2 × 3 × 3 = 36.

LCM of 3, 6, 9, and 12 by Prime Factorization

Prime factorization of 3, 6, 9, and 12 is (3) = 3¹, (2 × 3) = 2¹ × 3¹, (3 × 3) = 3², and (2 × 2 × 3) = 2² × 3¹ respectively. LCM of 3, 6, 9, and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² = 36.
Hence, the LCM of 3, 6, 9, and 12 by prime factorization is 36.

LCM of 3, 6, 9, and 12 by Listing Multiples

To calculate the LCM of 3, 6, 9, 12 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, 15 . . .), 6 (6, 12, 18, 24, 30 . . .), 9 (9, 18, 27, 36, 45 . . .), and 12 (12, 24, 36, 48, 60 . . .).
• Step 2: The common multiples from the multiples of 3, 6, 9, and 12 are 36, 72, . . .
• Step 3: The smallest common multiple of 3, 6, 9, and 12 is 36.

∴ The least common multiple of 3, 6, 9, and 12 = 36.

☛ Also Check:

• LCM of 24, 36, 44 and 62 - 24552
• LCM of 60 and 75 - 300
• LCM of 13 and 11 - 143
• LCM of 25 and 75 - 75
• LCM of 16 and 64 - 64
• LCM of 48 and 56 - 336
• LCM of 6, 12, 18 and 24 - 72

FAQs on LCM of 3, 6, 9, and 12

What is the LCM of 3, 6, 9, and 12?

The LCM of 3, 6, 9, and 12 is 36. To find the least common multiple of 3, 6, 9, and 12, we need to find the multiples of 3, 6, 9, and 12 (multiples of 3 = 3, 6, 9, 12 . . . . 36 . . . . ; multiples of 6 = 6, 12, 18, 24, 36 . . . .; multiples of 9 = 9, 18, 27, 36 . . . .; multiples of 12 = 12, 24, 36, 48 . . . .) and choose the smallest multiple that is exactly divisible by 3, 6, 9, and 12, i.e., 36.

How to Find the LCM of 3, 6, 9, and 12 by Prime Factorization?

To find the LCM of 3, 6, 9, and 12 using prime factorization, we will find the prime factors, (3 = 3¹), (6 = 2¹ × 3¹), (9 = 3²), and (12 = 2² × 3¹). LCM of 3, 6, 9, and 12 is the product of prime factors raised to their respective highest exponent among the numbers 3, 6, 9, and 12.
⇒ LCM of 3, 6, 9, 12 = 2² × 3² = 36.

Which of the following is the LCM of 3, 6, 9, and 12? 36, 10, 3, 25

The value of LCM of 3, 6, 9, 12 is the smallest common multiple of 3, 6, 9, and 12. The number satisfying the given condition is 36.

What are the Methods to Find LCM of 3, 6, 9, 12?

The commonly used methods to find the LCM of 3, 6, 9, 12 are:

• Listing Multiples
• Division Method
• Prime Factorization Method