Least Common Multiple of 345 and 349

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 345 and 349 the smallest integer that is 120405 that is divisible by both numbers.

Least Common Multiple (LCM) of 345 and 349 is 120405.

LCM(345,349) = 120405

LCM of 345 and 349

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

LCM of:
and

Least Common Multiple of 345 and 349

LCM of 345 and 349 is 120405

Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 349. First we will calculate the prime factors of 345 and 349.

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

Prime Factorization of 349


349 349
1

Prime factors of 349 are 349. Prime factorization of 349 in exponential form is:

349 = 3491

Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 349.

LCM(345,349) = 31×51×231×3491
LCM(345,349) = 120405

Factors of 345

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

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

Factors of 349

List of positive integer factors of 349 that divides 349 without a remainder.

1, 349

Least Common Multiple of 345 and 349 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 345 and 349, than apply into the LCM equation.

GCF(345,349) = 1
LCM(345,349) = ( 345 × 349) / 1
LCM(345,349) = 120405 / 1
LCM(345,349) = 120405

Properties of LCM 345 and 349

(i) The LCM of 349 and 345 is associative

LCM of 345 and 349 = LCM of 349 and 345

Related Least Common Multiples of 345

Related Least Common Multiples of 349

Frequently Asked Questions on LCM of 345 and 349

1. What is the LCM of 345 and 349?

Answer: LCM of 345 and 349 is 120405.

2. 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.

3. What are the Factors of 349?

Answer: Factors of 349 are 1, 349. There are 2 integers that are factors of 349. The greatest factor of 349 is 349.

4. How to Find the LCM of 345 and 349?

Answer:

Least Common Multiple of 345 and 349 = 120405

Step 1: Find the prime factorization of 345

345 = 3 x 5 x 23

Step 2: Find the prime factorization of 349

349 = 349

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

LCM = 120405 = 3 x 5 x 23 x 349

Step 4: Therefore, the least common multiple of 345 and 349 is 120405.