Least Common Multiple of 315 and 321

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 315 and 321 the smallest integer that is 33705 that is divisible by both numbers.

Least Common Multiple (LCM) of 315 and 321 is 33705.

LCM(315,321) = 33705

LCM of 315 and 321

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

LCM of:
and

Least Common Multiple of 315 and 321

LCM of 315 and 321 is 33705

Least common multiple can be found by multiplying the highest exponent prime factors of 315 and 321. First we will calculate the prime factors of 315 and 321.

Prime Factorization of 315


3 315
3 105
5 35
7 7
1

Prime factors of 315 are 3, 5,7. Prime factorization of 315 in exponential form is:

315 = 32×51×71

Prime Factorization of 321


3 321
107 107
1

Prime factors of 321 are 3,107. Prime factorization of 321 in exponential form is:

321 = 31×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 315 and 321.

LCM(315,321) = 32×51×71×1071
LCM(315,321) = 33705

Factors of 315

List of positive integer factors of 315 that divides 315 without a remainder.

1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315

Factors of 321

List of positive integer factors of 321 that divides 321 without a remainder.

1, 3, 107, 321

Least Common Multiple of 315 and 321 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 315 and 321, than apply into the LCM equation.

GCF(315,321) = 3
LCM(315,321) = ( 315 × 321) / 3
LCM(315,321) = 101115 / 3
LCM(315,321) = 33705

Properties of LCM 315 and 321

(i) The LCM of 321 and 315 is associative

LCM of 315 and 321 = LCM of 321 and 315

Related Least Common Multiples of 315

Related Least Common Multiples of 321

Frequently Asked Questions on LCM of 315 and 321

1. What is the LCM of 315 and 321?

Answer: LCM of 315 and 321 is 33705.

2. What are the Factors of 315?

Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.

3. What are the Factors of 321?

Answer: Factors of 321 are 1, 3, 107, 321. There are 4 integers that are factors of 321. The greatest factor of 321 is 321.

4. How to Find the LCM of 315 and 321?

Answer:

Least Common Multiple of 315 and 321 = 33705

Step 1: Find the prime factorization of 315

315 = 3 x 3 x 5 x 7

Step 2: Find the prime factorization of 321

321 = 3 x 107

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

LCM = 33705 = 3 x 3 x 5 x 7 x 107

Step 4: Therefore, the least common multiple of 315 and 321 is 33705.