Least Common Multiple of 345 and 352

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 352 the smallest integer that is 121440 that is divisible by both numbers.

Least Common Multiple (LCM) of 345 and 352 is 121440.

LCM(345,352) = 121440

LCM of 345 and 352

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

LCM of:
and

Least Common Multiple of 345 and 352

LCM of 345 and 352 is 121440

Least common multiple can be found by multiplying the highest exponent prime factors of 345 and 352. First we will calculate the prime factors of 345 and 352.

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 352


2 352
2 176
2 88
2 44
2 22
11 11
1

Prime factors of 352 are 2,11. Prime factorization of 352 in exponential form is:

352 = 25×111

Now multiplying the highest exponent prime factors to calculate the LCM of 345 and 352.

LCM(345,352) = 25×31×51×111×231
LCM(345,352) = 121440

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 352

List of positive integer factors of 352 that divides 352 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352

Least Common Multiple of 345 and 352 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 352, than apply into the LCM equation.

GCF(345,352) = 1
LCM(345,352) = ( 345 × 352) / 1
LCM(345,352) = 121440 / 1
LCM(345,352) = 121440

Properties of LCM 345 and 352

(i) The LCM of 352 and 345 is associative

LCM of 345 and 352 = LCM of 352 and 345

Related Least Common Multiples of 345

Related Least Common Multiples of 352

Frequently Asked Questions on LCM of 345 and 352

1. What is the LCM of 345 and 352?

Answer: LCM of 345 and 352 is 121440.

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 352?

Answer: Factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352. There are 12 integers that are factors of 352. The greatest factor of 352 is 352.

4. How to Find the LCM of 345 and 352?

Answer:

Least Common Multiple of 345 and 352 = 121440

Step 1: Find the prime factorization of 345

345 = 3 x 5 x 23

Step 2: Find the prime factorization of 352

352 = 2 x 2 x 2 x 2 x 2 x 11

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

LCM = 121440 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 11 x 23

Step 4: Therefore, the least common multiple of 345 and 352 is 121440.