Orchids Logo
Admissions 2025-26
9-999-431-999info@orchids.edu.inWhatsapp
Login
Doubt Connect
Orchids Logo

LCM of 336 and 54: How to find LCM of 336 and 54?

The LCM of 336 and 54 is 3024. Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both. The LCM of 336 and 54 is the smallest number that both 336 and 54 fit into. In this blog, we’ll explain easy ways to find the LCM of 336 and 54.

Methods to find the LCM of 336 and 54

Here are three simple methods to find the LCM of 336 and 54:

1. Prime Factorization Method

We break each number into its prime factors and take the highest power of each factor.

  • 336 = 2 × 2 × 2 × 2 × 3 × 7
  • 54 = 2 × 3 × 3 × 3
  • Taking the highest powers: 2⁴ × 3³ × 7 = 3024

Thus, LCM(336,54) = 3024.

2. Listing Multiples Method

We list the multiples of both numbers and find the smallest one they share.

  • Multiples of 336: 336, 672, 1008, 1344, 1680, 2016, 2352, 2688, 3024, ...
  • Multiples of 54: 54, 108, 162, 216, 270, 324, ..., 3024, ...
  • The smallest common multiple is 3024.

Thus, LCM(336,54) = 3024.

3. Division Method

We divide both numbers by their common factors until at least 2 numbers are divisible.

  1. Divide 336 and 54 by 2 → (168, 27)
  2. Divide 168 and 27 by 3 → (56, 9)
  3. Both 56 and 9 are divisible only by 1.
  4. Multiply the divisors: 2 × 3 × 56 × 9 = 3024

Thus, LCM(336,54) = 3024.

Know how to find the lcm of 510 and 92 here.

Conclusion:

The LCM of 336 and 54 is 3024, and you can find it using prime factorization, listing multiples, or division. These methods make LCM calculations simple and useful.

FAQs

1. What is the LCM of 336 and 54?

The LCM of 336 and 54 is 3,024. This is the smallest positive integer that is divisible by both 336 and 54 without leaving any remainder. 

2. How to Find the LCM of 336 and 54 Using Prime Factorization?

To find the LCM using prime factorization:

  • Prime factorization of 336: 2⁴ × 3 × 7

  • Prime factorization of 54: 2 × 3³​

The LCM is obtained by multiplying the highest powers of all prime factors present in either number:​

LCM = 2⁴ × 3³ × 7 = 3,024

3. How to Find the LCM of 336 and 54 Using the Division Method?

The division method involves dividing the numbers by their common prime factors:​

  • Divide both numbers by 2: 336 ÷ 2 = 168; 54 ÷ 2 = 27
  • Divide the resulting numbers by 3: 168 ÷ 3 = 56; 27 ÷ 3 = 9
  • Continue dividing by prime numbers until all resulting numbers are 1.
  • Multiply all the prime divisors used: 2 × 3 × 2 × 2 × 2 × 3 × 3 × 3 × 7 = 3,024
Share