Least Common Multiple of 338 and 342

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 342 the smallest integer that is 57798 that is divisible by both numbers.

Least Common Multiple (LCM) of 338 and 342 is 57798.

LCM(338,342) = 57798

LCM of 338 and 342

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

LCM of:
and

Least Common Multiple of 338 and 342

LCM of 338 and 342 is 57798

Least common multiple can be found by multiplying the highest exponent prime factors of 338 and 342. First we will calculate the prime factors of 338 and 342.

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 342


2 342
3 171
3 57
19 19
1

Prime factors of 342 are 2, 3,19. Prime factorization of 342 in exponential form is:

342 = 21×32×191

Now multiplying the highest exponent prime factors to calculate the LCM of 338 and 342.

LCM(338,342) = 21×32×132×191
LCM(338,342) = 57798

Factors of 338

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

1, 2, 13, 26, 169, 338

Factors of 342

List of positive integer factors of 342 that divides 342 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342

Least Common Multiple of 338 and 342 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 342, than apply into the LCM equation.

GCF(338,342) = 2
LCM(338,342) = ( 338 × 342) / 2
LCM(338,342) = 115596 / 2
LCM(338,342) = 57798

Properties of LCM 338 and 342

(i) The LCM of 342 and 338 is associative

LCM of 338 and 342 = LCM of 342 and 338

Related Least Common Multiples of 338

Related Least Common Multiples of 342

Frequently Asked Questions on LCM of 338 and 342

1. What is the LCM of 338 and 342?

Answer: LCM of 338 and 342 is 57798.

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 342?

Answer: Factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342. There are 12 integers that are factors of 342. The greatest factor of 342 is 342.

4. How to Find the LCM of 338 and 342?

Answer:

Least Common Multiple of 338 and 342 = 57798

Step 1: Find the prime factorization of 338

338 = 2 x 13 x 13

Step 2: Find the prime factorization of 342

342 = 2 x 3 x 3 x 19

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

LCM = 57798 = 2 x 3 x 3 x 13 x 13 x 19

Step 4: Therefore, the least common multiple of 338 and 342 is 57798.