Least Common Multiple of 342 and 345

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 342 and 345 the smallest integer that is 39330 that is divisible by both numbers.

Least Common Multiple (LCM) of 342 and 345 is 39330.

LCM(342,345) = 39330

LCM of 342 and 345

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

LCM of:
and

Least Common Multiple of 342 and 345

LCM of 342 and 345 is 39330

Least common multiple can be found by multiplying the highest exponent prime factors of 342 and 345. First we will calculate the prime factors of 342 and 345.

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

Prime Factorization of 345


3 345
5 115
23 23
1

Prime factors of 345 are 3, 5,23. Prime factorization of 345 in exponential form is:

345 = 31×51×231

Now multiplying the highest exponent prime factors to calculate the LCM of 342 and 345.

LCM(342,345) = 21×32×51×191×231
LCM(342,345) = 39330

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

Factors of 345

List of positive integer factors of 345 that divides 345 without a remainder.

1, 3, 5, 15, 23, 69, 115, 345

Least Common Multiple of 342 and 345 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 342 and 345, than apply into the LCM equation.

GCF(342,345) = 3
LCM(342,345) = ( 342 × 345) / 3
LCM(342,345) = 117990 / 3
LCM(342,345) = 39330

Properties of LCM 342 and 345

(i) The LCM of 345 and 342 is associative

LCM of 342 and 345 = LCM of 345 and 342

Related Least Common Multiples of 342

Related Least Common Multiples of 345

Frequently Asked Questions on LCM of 342 and 345

1. What is the LCM of 342 and 345?

Answer: LCM of 342 and 345 is 39330.

2. 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.

3. What are the Factors of 345?

Answer: Factors of 345 are 1, 3, 5, 15, 23, 69, 115, 345. There are 8 integers that are factors of 345. The greatest factor of 345 is 345.

4. How to Find the LCM of 342 and 345?

Answer:

Least Common Multiple of 342 and 345 = 39330

Step 1: Find the prime factorization of 342

342 = 2 x 3 x 3 x 19

Step 2: Find the prime factorization of 345

345 = 3 x 5 x 23

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

LCM = 39330 = 2 x 3 x 3 x 5 x 19 x 23

Step 4: Therefore, the least common multiple of 342 and 345 is 39330.