LCM of 16 and 21

LCM of 16 and 21 is the smallest number among all common multiples of 16 and 21. The first few multiples of 16 and 21 are (16, 32, 48, 64, 80, 96, . . . ) and (21, 42, 63, 84, 105, 126, 147, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 21 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 16 and 21 is 336.

Explanation:

The LCM of two non-zero integers, x(16) and y(21), is the smallest positive integer m(336) that is divisible by both x(16) and y(21) without any remainder.

The methods to find the LCM of 16 and 21 are explained below.

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

LCM of 16 and 21 by Listing Multiples

To calculate the LCM of 16 and 21 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 21 (21, 42, 63, 84, 105, 126, 147, . . . . )
• Step 2: The common multiples from the multiples of 16 and 21 are 336, 672, . . .
• Step 3: The smallest common multiple of 16 and 21 is 336.

∴ The least common multiple of 16 and 21 = 336.

LCM of 16 and 21 by Prime Factorization

Prime factorization of 16 and 21 is (2 × 2 × 2 × 2) = 2⁴ and (3 × 7) = 3¹ × 7¹ respectively. LCM of 16 and 21 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 21 by prime factorization is 336.

LCM of 16 and 21 by Division Method

To calculate the LCM of 16 and 21 by the division method, we will divide the numbers(16, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 21.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 21. Write this prime number(2) on the left of the given numbers(16 and 21), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (16, 21) 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 21 is the product of all prime numbers on the left, i.e. LCM(16, 21) by division method = 2 × 2 × 2 × 2 × 3 × 7 = 336.

☛ Also Check:

• LCM of 72 and 84 - 504
• LCM of 4, 6 and 8 - 24
• LCM of 15 and 45 - 45
• LCM of 4 and 6 - 12
• LCM of 8, 12 and 15 - 120
• LCM of 7 and 12 - 84
• LCM of 60 and 90 - 180

FAQs on LCM of 16 and 21

What is the LCM of 16 and 21?

The LCM of 16 and 21 is 336. To find the least common multiple of 16 and 21, we need to find the multiples of 16 and 21 (multiples of 16 = 16, 32, 48, 64 . . . . 336; multiples of 21 = 21, 42, 63, 84 . . . . 336) and choose the smallest multiple that is exactly divisible by 16 and 21, i.e., 336.

Which of the following is the LCM of 16 and 21? 15, 2, 42, 336

The value of LCM of 16, 21 is the smallest common multiple of 16 and 21. The number satisfying the given condition is 336.

If the LCM of 21 and 16 is 336, Find its GCF.

LCM(21, 16) × GCF(21, 16) = 21 × 16
Since the LCM of 21 and 16 = 336
⇒ 336 × GCF(21, 16) = 336
Therefore, the GCF = 336/336 = 1.

What is the Least Perfect Square Divisible by 16 and 21?

The least number divisible by 16 and 21 = LCM(16, 21)
LCM of 16 and 21 = 2 × 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7]
⇒ Least perfect square divisible by each 16 and 21 = LCM(16, 21) × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.

What is the Relation Between GCF and LCM of 16, 21?

The following equation can be used to express the relation between GCF and LCM of 16 and 21, i.e. GCF × LCM = 16 × 21.