Least Common Multiple of 338 and 340

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 340 the smallest integer that is 57460 that is divisible by both numbers.

Least Common Multiple (LCM) of 338 and 340 is 57460.

LCM(338,340) = 57460

LCM of 338 and 340

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

LCM of:
and

Least Common Multiple of 338 and 340

LCM of 338 and 340 is 57460

Least common multiple can be found by multiplying the highest exponent prime factors of 338 and 340. First we will calculate the prime factors of 338 and 340.

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 340


2 340
2 170
5 85
17 17
1

Prime factors of 340 are 2, 5,17. Prime factorization of 340 in exponential form is:

340 = 22×51×171

Now multiplying the highest exponent prime factors to calculate the LCM of 338 and 340.

LCM(338,340) = 22×51×132×171
LCM(338,340) = 57460

Factors of 338

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

1, 2, 13, 26, 169, 338

Factors of 340

List of positive integer factors of 340 that divides 340 without a remainder.

1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340

Least Common Multiple of 338 and 340 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 340, than apply into the LCM equation.

GCF(338,340) = 2
LCM(338,340) = ( 338 × 340) / 2
LCM(338,340) = 114920 / 2
LCM(338,340) = 57460

Properties of LCM 338 and 340

(i) The LCM of 340 and 338 is associative

LCM of 338 and 340 = LCM of 340 and 338

Related Least Common Multiples of 338

Related Least Common Multiples of 340

Frequently Asked Questions on LCM of 338 and 340

1. What is the LCM of 338 and 340?

Answer: LCM of 338 and 340 is 57460.

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 340?

Answer: Factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340. There are 12 integers that are factors of 340. The greatest factor of 340 is 340.

4. How to Find the LCM of 338 and 340?

Answer:

Least Common Multiple of 338 and 340 = 57460

Step 1: Find the prime factorization of 338

338 = 2 x 13 x 13

Step 2: Find the prime factorization of 340

340 = 2 x 2 x 5 x 17

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

LCM = 57460 = 2 x 2 x 5 x 13 x 13 x 17

Step 4: Therefore, the least common multiple of 338 and 340 is 57460.