Least Common Multiple of 345 and 351

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 351 the smallest integer that is 40365 that is divisible by both numbers.

Least Common Multiple (LCM) of 345 and 351 is 40365.

LCM(345,351) = 40365

LCM of 345 and 351

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

LCM of:
and

Least Common Multiple of 345 and 351

LCM of 345 and 351 is 40365

Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 351. First we will calculate the prime factors of 345 and 351.

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 351


3 351
3 117
3 39
13 13
1

Prime factors of 351 are 3,13. Prime factorization of 351 in exponential form is:

351 = 33×131

Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 351.

LCM(345,351) = 33×51×131×231
LCM(345,351) = 40365

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 351

List of positive integer factors of 351 that divides 351 without a remainder.

1, 3, 9, 13, 27, 39, 117, 351

Least Common Multiple of 345 and 351 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 351, than apply into the LCM equation.

GCF(345,351) = 3
LCM(345,351) = ( 345 × 351) / 3
LCM(345,351) = 121095 / 3
LCM(345,351) = 40365

Properties of LCM 345 and 351

(i) The LCM of 351 and 345 is associative

LCM of 345 and 351 = LCM of 351 and 345

Related Least Common Multiples of 345

Related Least Common Multiples of 351

Frequently Asked Questions on LCM of 345 and 351

1. What is the LCM of 345 and 351?

Answer: LCM of 345 and 351 is 40365.

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 351?

Answer: Factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351. There are 8 integers that are factors of 351. The greatest factor of 351 is 351.

4. How to Find the LCM of 345 and 351?

Answer:

Least Common Multiple of 345 and 351 = 40365

Step 1: Find the prime factorization of 345

345 = 3 x 5 x 23

Step 2: Find the prime factorization of 351

351 = 3 x 3 x 3 x 13

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

LCM = 40365 = 3 x 3 x 3 x 5 x 13 x 23

Step 4: Therefore, the least common multiple of 345 and 351 is 40365.