LCM of 12 and 42

LCM of 12 and 42 is the smallest number among all common multiples of 12 and 42. The first few multiples of 12 and 42 are (12, 24, 36, 48, 60, 72, . . . ) and (42, 84, 126, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 42 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 12 and 42 is 84.

Explanation:

The LCM of two non-zero integers, x(12) and y(42), is the smallest positive integer m(84) that is divisible by both x(12) and y(42) without any remainder.

Let's look at the different methods for finding the LCM of 12 and 42.

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

LCM of 12 and 42 by Prime Factorization

Prime factorization of 12 and 42 is (2 × 2 × 3) = 2² × 3¹ and (2 × 3 × 7) = 2¹ × 3¹ × 7¹ respectively. LCM of 12 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 7¹ = 84.
Hence, the LCM of 12 and 42 by prime factorization is 84.

LCM of 12 and 42 by Listing Multiples

To calculate the LCM of 12 and 42 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, . . . ) and 42 (42, 84, 126, 168, . . . . )
• Step 2: The common multiples from the multiples of 12 and 42 are 84, 168, . . .
• Step 3: The smallest common multiple of 12 and 42 is 84.

∴ The least common multiple of 12 and 42 = 84.

LCM of 12 and 42 by Division Method

To calculate the LCM of 12 and 42 by the division method, we will divide the numbers(12, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 42.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 42. Write this prime number(2) on the left of the given numbers(12 and 42), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 42) 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 42 is the product of all prime numbers on the left, i.e. LCM(12, 42) by division method = 2 × 2 × 3 × 7 = 84.

☛ Also Check:

• LCM of 9, 12 and 18 - 36
• LCM of 9, 12 and 15 - 180
• LCM of 84, 90 and 120 - 2520
• LCM of 80, 85 and 90 - 12240
• LCM of 8, 9 and 10 - 360
• LCM of 8, 9 and 25 - 1800
• LCM of 8, 9 and 12 - 72

FAQs on LCM of 12 and 42

What is the LCM of 12 and 42?

The LCM of 12 and 42 is 84. To find the least common multiple of 12 and 42, we need to find the multiples of 12 and 42 (multiples of 12 = 12, 24, 36, 48 . . . . 84; multiples of 42 = 42, 84, 126, 168) and choose the smallest multiple that is exactly divisible by 12 and 42, i.e., 84.

What is the Least Perfect Square Divisible by 12 and 42?

The least number divisible by 12 and 42 = LCM(12, 42)
LCM of 12 and 42 = 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7]
⇒ Least perfect square divisible by each 12 and 42 = LCM(12, 42) × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

Which of the following is the LCM of 12 and 42? 84, 10, 11, 18

The value of LCM of 12, 42 is the smallest common multiple of 12 and 42. The number satisfying the given condition is 84.

How to Find the LCM of 12 and 42 by Prime Factorization?

To find the LCM of 12 and 42 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (42 = 2 × 3 × 7). LCM of 12 and 42 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 42.
⇒ LCM of 12, 42 = 2² × 3¹ × 7¹ = 84.

If the LCM of 42 and 12 is 84, Find its GCF.

LCM(42, 12) × GCF(42, 12) = 42 × 12
Since the LCM of 42 and 12 = 84
⇒ 84 × GCF(42, 12) = 504
Therefore, the greatest common factor = 504/84 = 6.