LCM of 8 and 42

LCM of 8 and 42 is the smallest number among all common multiples of 8 and 42. The first few multiples of 8 and 42 are (8, 16, 24, 32, 40, 48, . . . ) and (42, 84, 126, 168, 210, 252, 294, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 42 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 8 and 42 is 168.

Explanation:

The LCM of two non-zero integers, x(8) and y(42), is the smallest positive integer m(168) that is divisible by both x(8) and y(42) without any remainder.

Let's look at the different methods for finding the LCM of 8 and 42.

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

LCM of 8 and 42 by Listing Multiples

To calculate the LCM of 8 and 42 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 42 (42, 84, 126, 168, 210, 252, 294, . . . . )
• Step 2: The common multiples from the multiples of 8 and 42 are 168, 336, . . .
• Step 3: The smallest common multiple of 8 and 42 is 168.

∴ The least common multiple of 8 and 42 = 168.

LCM of 8 and 42 by Prime Factorization

Prime factorization of 8 and 42 is (2 × 2 × 2) = 2³ and (2 × 3 × 7) = 2¹ × 3¹ × 7¹ respectively. LCM of 8 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 7¹ = 168.
Hence, the LCM of 8 and 42 by prime factorization is 168.

LCM of 8 and 42 by Division Method

To calculate the LCM of 8 and 42 by the division method, we will divide the numbers(8, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 42.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 42. Write this prime number(2) on the left of the given numbers(8 and 42), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 42 is the product of all prime numbers on the left, i.e. LCM(8, 42) by division method = 2 × 2 × 2 × 3 × 7 = 168.

☛ Also Check:

• LCM of 10 and 25 - 50
• LCM of 10 and 16 - 80
• LCM of 2, 5 and 6 - 30
• LCM of 36 and 81 - 324
• LCM of 40, 48 and 45 - 720
• LCM of 42 and 70 - 210
• LCM of 7 and 10 - 70

FAQs on LCM of 8 and 42

What is the LCM of 8 and 42?

The LCM of 8 and 42 is 168. To find the least common multiple (LCM) of 8 and 42, we need to find the multiples of 8 and 42 (multiples of 8 = 8, 16, 24, 32 . . . . 168; multiples of 42 = 42, 84, 126, 168) and choose the smallest multiple that is exactly divisible by 8 and 42, i.e., 168.

How to Find the LCM of 8 and 42 by Prime Factorization?

To find the LCM of 8 and 42 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (42 = 2 × 3 × 7). LCM of 8 and 42 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 42.
⇒ LCM of 8, 42 = 2³ × 3¹ × 7¹ = 168.

What is the Least Perfect Square Divisible by 8 and 42?

The least number divisible by 8 and 42 = LCM(8, 42)
LCM of 8 and 42 = 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 8 and 42 = LCM(8, 42) × 2 × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.

If the LCM of 42 and 8 is 168, Find its GCF.

LCM(42, 8) × GCF(42, 8) = 42 × 8
Since the LCM of 42 and 8 = 168
⇒ 168 × GCF(42, 8) = 336
Therefore, the greatest common factor (GCF) = 336/168 = 2.

What is the Relation Between GCF and LCM of 8, 42?

The following equation can be used to express the relation between GCF and LCM of 8 and 42, i.e. GCF × LCM = 8 × 42.