Least Common Multiple of 315 and 693

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 693 the smallest integer that is 3465 that is divisible by both numbers.

Least Common Multiple (LCM) of 315 and 693 is 3465.

LCM(315,693) = 3465

LCM of 315 and 693

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

LCM of:
and

Least Common Multiple of 315 and 693

LCM of 315 and 693 is 3465

Least common multiple can be found by multiplying the highest exponent prime factors of 315 and 693. First we will calculate the prime factors of 315 and 693.

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 693


3 693
3 231
7 77
11 11
1

Prime factors of 693 are 3, 7,11. Prime factorization of 693 in exponential form is:

693 = 32×71×111

Now multiplying the highest exponent prime factors to calculate the LCM of 315 and 693.

LCM(315,693) = 32×51×71×111
LCM(315,693) = 3465

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 693

List of positive integer factors of 693 that divides 693 without a remainder.

1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693

Least Common Multiple of 315 and 693 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 693, than apply into the LCM equation.

GCF(315,693) = 63
LCM(315,693) = ( 315 × 693) / 63
LCM(315,693) = 218295 / 63
LCM(315,693) = 3465

Properties of LCM 315 and 693

(i) The LCM of 693 and 315 is associative

LCM of 315 and 693 = LCM of 693 and 315

Related Least Common Multiples of 315

Related Least Common Multiples of 693

Frequently Asked Questions on LCM of 315 and 693

1. What is the LCM of 315 and 693?

Answer: LCM of 315 and 693 is 3465.

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 693?

Answer: Factors of 693 are 1, 3, 7, 9, 11, 21, 33, 63, 77, 99, 231, 693. There are 12 integers that are factors of 693. The greatest factor of 693 is 693.

4. How to Find the LCM of 315 and 693?

Answer:

Least Common Multiple of 315 and 693 = 3465

Step 1: Find the prime factorization of 315

315 = 3 x 3 x 5 x 7

Step 2: Find the prime factorization of 693

693 = 3 x 3 x 7 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 = 3465 = 3 x 3 x 5 x 7 x 11

Step 4: Therefore, the least common multiple of 315 and 693 is 3465.