Least Common Multiple of 338 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 338 and 343 the smallest integer that is 115934 that is divisible by both numbers.

Least Common Multiple (LCM) of 338 and 343 is 115934.

LCM(338,343) = 115934

LCM of 338 and 343

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

LCM of:
and

Least Common Multiple of 338 and 343

LCM of 338 and 343 is 115934

Least common multiple can be found by multiplying the highest exponent prime factors of 338 and 343. First we will calculate the prime factors of 338 and 343.

Prime Factorization of 338


2 338
13 169
13 13
1

Prime factors of 338 are 2,13. Prime factorization of 338 in exponential form is:

338 = 21×132

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 338 and 343.

LCM(338,343) = 21×73×132
LCM(338,343) = 115934

Factors of 338

List of positive integer factors of 338 that divides 338 without a remainder.

1, 2, 13, 26, 169, 338

Factors of 343

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

1, 7, 49, 343

Least Common Multiple of 338 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 338 and 343, than apply into the LCM equation.

GCF(338,343) = 1
LCM(338,343) = ( 338 × 343) / 1
LCM(338,343) = 115934 / 1
LCM(338,343) = 115934

Properties of LCM 338 and 343

(i) The LCM of 343 and 338 is associative

LCM of 338 and 343 = LCM of 343 and 338

Related Least Common Multiples of 338

Related Least Common Multiples of 343

Frequently Asked Questions on LCM of 338 and 343

1. What is the LCM of 338 and 343?

Answer: LCM of 338 and 343 is 115934.

2. What are the Factors of 338?

Answer: Factors of 338 are 1, 2, 13, 26, 169, 338. There are 6 integers that are factors of 338. The greatest factor of 338 is 338.

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 338 and 343?

Answer:

Least Common Multiple of 338 and 343 = 115934

Step 1: Find the prime factorization of 338

338 = 2 x 13 x 13

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 = 115934 = 2 x 7 x 7 x 7 x 13 x 13

Step 4: Therefore, the least common multiple of 338 and 343 is 115934.