Least Common Multiple of 345 and 346

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 346 the smallest integer that is 119370 that is divisible by both numbers.

Least Common Multiple (LCM) of 345 and 346 is 119370.

LCM(345,346) = 119370

LCM of 345 and 346

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

LCM of:
and

Least Common Multiple of 345 and 346

LCM of 345 and 346 is 119370

Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 346. First we will calculate the prime factors of 345 and 346.

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 346


2 346
173 173
1

Prime factors of 346 are 2,173. Prime factorization of 346 in exponential form is:

346 = 21×1731

Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 346.

LCM(345,346) = 21×31×51×231×1731
LCM(345,346) = 119370

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 346

List of positive integer factors of 346 that divides 346 without a remainder.

1, 2, 173, 346

Least Common Multiple of 345 and 346 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 346, than apply into the LCM equation.

GCF(345,346) = 1
LCM(345,346) = ( 345 × 346) / 1
LCM(345,346) = 119370 / 1
LCM(345,346) = 119370

Properties of LCM 345 and 346

(i) The LCM of 346 and 345 is associative

LCM of 345 and 346 = LCM of 346 and 345

Related Least Common Multiples of 345

Related Least Common Multiples of 346

Frequently Asked Questions on LCM of 345 and 346

1. What is the LCM of 345 and 346?

Answer: LCM of 345 and 346 is 119370.

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 346?

Answer: Factors of 346 are 1, 2, 173, 346. There are 4 integers that are factors of 346. The greatest factor of 346 is 346.

4. How to Find the LCM of 345 and 346?

Answer:

Least Common Multiple of 345 and 346 = 119370

Step 1: Find the prime factorization of 345

345 = 3 x 5 x 23

Step 2: Find the prime factorization of 346

346 = 2 x 173

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

LCM = 119370 = 2 x 3 x 5 x 23 x 173

Step 4: Therefore, the least common multiple of 345 and 346 is 119370.