Least Common Multiple of 336 and 343

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 336 and 343 the smallest integer that is 16464 that is divisible by both numbers.

Least Common Multiple (LCM) of 336 and 343 is 16464.

LCM(336,343) = 16464

LCM of 336 and 343

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 336 and 343

LCM of 336 and 343 is 16464

Least common multiple can be found by multiplying the highest exponent prime factors of 336 and 343. First we will calculate the prime factors of 336 and 343.

Prime Factorization of 336


2 336
2 168
2 84
2 42
3 21
7 7
1

Prime factors of 336 are 2, 3,7. Prime factorization of 336 in exponential form is:

336 = 24×31×71

Prime Factorization of 343


7 343
7 49
7 7
1

Prime factors of 343 are 7. Prime factorization of 343 in exponential form is:

343 = 73

Now multiplying the highest exponent prime factors to calculate the LCM of 336 and 343.

LCM(336,343) = 24×31×73
LCM(336,343) = 16464

Factors of 336

List of positive integer factors of 336 that divides 336 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336

Factors of 343

List of positive integer factors of 343 that divides 343 without a remainder.

1, 7, 49, 343

Least Common Multiple of 336 and 343 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 336 and 343, than apply into the LCM equation.

GCF(336,343) = 7
LCM(336,343) = ( 336 × 343) / 7
LCM(336,343) = 115248 / 7
LCM(336,343) = 16464

Properties of LCM 336 and 343

(i) The LCM of 343 and 336 is associative

LCM of 336 and 343 = LCM of 343 and 336

Related Least Common Multiples of 336

Related Least Common Multiples of 343

Frequently Asked Questions on LCM of 336 and 343

1. What is the LCM of 336 and 343?

Answer: LCM of 336 and 343 is 16464.

2. What are the Factors of 336?

Answer: Factors of 336 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 56, 84, 112, 168, 336. There are 20 integers that are factors of 336. The greatest factor of 336 is 336.

3. What are the Factors of 343?

Answer: Factors of 343 are 1, 7, 49, 343. There are 4 integers that are factors of 343. The greatest factor of 343 is 343.

4. How to Find the LCM of 336 and 343?

Answer:

Least Common Multiple of 336 and 343 = 16464

Step 1: Find the prime factorization of 336

336 = 2 x 2 x 2 x 2 x 3 x 7

Step 2: Find the prime factorization of 343

343 = 7 x 7 x 7

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 16464 = 2 x 2 x 2 x 2 x 3 x 7 x 7 x 7

Step 4: Therefore, the least common multiple of 336 and 343 is 16464.