LCM of 16 and 42

LCM of 16 and 42 is the smallest number among all common multiples of 16 and 42. The first few multiples of 16 and 42 are (16, 32, 48, 64, 80, 96, . . . ) and (42, 84, 126, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 42 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 16 and 42 is 336.

Explanation:

The LCM of two non-zero integers, x(16) and y(42), is the smallest positive integer m(336) that is divisible by both x(16) and y(42) without any remainder.

Let's look at the different methods for finding the LCM of 16 and 42.

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

LCM of 16 and 42 by Listing Multiples

To calculate the LCM of 16 and 42 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 16 (16, 32, 48, 64, 80, 96, . . . ) and 42 (42, 84, 126, 168, . . . . )
• Step 2: The common multiples from the multiples of 16 and 42 are 336, 672, . . .
• Step 3: The smallest common multiple of 16 and 42 is 336.

∴ The least common multiple of 16 and 42 = 336.

LCM of 16 and 42 by Prime Factorization

Prime factorization of 16 and 42 is (2 × 2 × 2 × 2) = 2⁴ and (2 × 3 × 7) = 2¹ × 3¹ × 7¹ respectively. LCM of 16 and 42 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 7¹ = 336.
Hence, the LCM of 16 and 42 by prime factorization is 336.

LCM of 16 and 42 by Division Method

To calculate the LCM of 16 and 42 by the division method, we will divide the numbers(16, 42) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 42.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 42. Write this prime number(2) on the left of the given numbers(16 and 42), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 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 16 and 42 is the product of all prime numbers on the left, i.e. LCM(16, 42) by division method = 2 × 2 × 2 × 2 × 3 × 7 = 336.

☛ Also Check:

• LCM of 404 and 96 - 9696
• LCM of 24 and 56 - 168
• LCM of 2, 5 and 6 - 30
• LCM of 8 and 25 - 200
• LCM of 8, 10 and 12 - 120
• LCM of 200 and 300 - 600
• LCM of 18 and 24 - 72

FAQs on LCM of 16 and 42

What is the LCM of 16 and 42?

The LCM of 16 and 42 is 336. To find the LCM (least common multiple) of 16 and 42, we need to find the multiples of 16 and 42 (multiples of 16 = 16, 32, 48, 64 . . . . 336; multiples of 42 = 42, 84, 126, 168 . . . . 336) and choose the smallest multiple that is exactly divisible by 16 and 42, i.e., 336.

What is the Relation Between GCF and LCM of 16, 42?

The following equation can be used to express the relation between GCF and LCM of 16 and 42, i.e. GCF × LCM = 16 × 42.

Which of the following is the LCM of 16 and 42? 15, 336, 20, 30

The value of LCM of 16, 42 is the smallest common multiple of 16 and 42. The number satisfying the given condition is 336.

How to Find the LCM of 16 and 42 by Prime Factorization?

To find the LCM of 16 and 42 using prime factorization, we will find the prime factors, (16 = 2 × 2 × 2 × 2) and (42 = 2 × 3 × 7). LCM of 16 and 42 is the product of prime factors raised to their respective highest exponent among the numbers 16 and 42.
⇒ LCM of 16, 42 = 2⁴ × 3¹ × 7¹ = 336.

If the LCM of 42 and 16 is 336, Find its GCF.

LCM(42, 16) × GCF(42, 16) = 42 × 16
Since the LCM of 42 and 16 = 336
⇒ 336 × GCF(42, 16) = 672
Therefore, the GCF (greatest common factor) = 672/336 = 2.