LCM of 28 and 42

LCM of 28 and 42 is the smallest number among all common multiples of 28 and 42. The first few multiples of 28 and 42 are (28, 56, 84, 112, 140, 168, 196, . . . ) and (42, 84, 126, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 28 and 42 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 28 and 42 is 84.

Explanation:

The LCM of two non-zero integers, x(28) and y(42), is the smallest positive integer m(84) that is divisible by both x(28) and y(42) without any remainder.

Let's look at the different methods for finding the LCM of 28 and 42.

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

LCM of 28 and 42 by Listing Multiples

To calculate the LCM of 28 and 42 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 28 (28, 56, 84, 112, 140, 168, 196, . . . ) and 42 (42, 84, 126, 168, . . . . )
• Step 2: The common multiples from the multiples of 28 and 42 are 84, 168, . . .
• Step 3: The smallest common multiple of 28 and 42 is 84.

∴ The least common multiple of 28 and 42 = 84.

LCM of 28 and 42 by Prime Factorization

Prime factorization of 28 and 42 is (2 × 2 × 7) = 2² × 7¹ and (2 × 3 × 7) = 2¹ × 3¹ × 7¹ respectively. LCM of 28 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 28 and 42 by prime factorization is 84.

LCM of 28 and 42 by Division Method

To calculate the LCM of 28 and 42 by the division method, we will divide the numbers(28, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 28 and 42.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 28 and 42. Write this prime number(2) on the left of the given numbers(28 and 42), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (28, 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 28 and 42 is the product of all prime numbers on the left, i.e. LCM(28, 42) by division method = 2 × 2 × 3 × 7 = 84.

☛ Also Check:

• LCM of 9 and 24 - 72
• LCM of 40, 42 and 45 - 2520
• LCM of 2, 3 and 4 - 12
• LCM of 37 and 49 - 1813
• LCM of 30 and 75 - 150
• LCM of 6, 15 and 18 - 90
• LCM of 4, 7 and 14 - 28

FAQs on LCM of 28 and 42

What is the LCM of 28 and 42?

The LCM of 28 and 42 is 84. To find the LCM (least common multiple) of 28 and 42, we need to find the multiples of 28 and 42 (multiples of 28 = 28, 56, 84, 112; multiples of 42 = 42, 84, 126, 168) and choose the smallest multiple that is exactly divisible by 28 and 42, i.e., 84.

Which of the following is the LCM of 28 and 42? 84, 42, 27, 18

The value of LCM of 28, 42 is the smallest common multiple of 28 and 42. The number satisfying the given condition is 84.

If the LCM of 42 and 28 is 84, Find its GCF.

LCM(42, 28) × GCF(42, 28) = 42 × 28
Since the LCM of 42 and 28 = 84
⇒ 84 × GCF(42, 28) = 1176
Therefore, the GCF = 1176/84 = 14.

What is the Least Perfect Square Divisible by 28 and 42?

The least number divisible by 28 and 42 = LCM(28, 42)
LCM of 28 and 42 = 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7]
⇒ Least perfect square divisible by each 28 and 42 = LCM(28, 42) × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

What is the Relation Between GCF and LCM of 28, 42?

The following equation can be used to express the relation between GCF and LCM of 28 and 42, i.e. GCF × LCM = 28 × 42.