Least Common Multiple of 390 and 396

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 390 and 396 the smallest integer that is 25740 that is divisible by both numbers.

Least Common Multiple (LCM) of 390 and 396 is 25740.

LCM(390,396) = 25740

LCM of 390 and 396

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

LCM of:
and

Least Common Multiple of 390 and 396

LCM of 390 and 396 is 25740

Least common multiple can be found by multiplying the highest exponent prime factors of 390 and 396. First we will calculate the prime factors of 390 and 396.

Prime Factorization of 390


2 390
3 195
5 65
13 13
1

Prime factors of 390 are 2, 3, 5,13. Prime factorization of 390 in exponential form is:

390 = 21×31×51×131

Prime Factorization of 396


2 396
2 198
3 99
3 33
11 11
1

Prime factors of 396 are 2, 3,11. Prime factorization of 396 in exponential form is:

396 = 22×32×111

Now multiplying the highest exponent prime factors to calculate the LCM of 390 and 396.

LCM(390,396) = 22×32×51×111×131
LCM(390,396) = 25740

Factors of 390

List of positive integer factors of 390 that divides 390 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390

Factors of 396

List of positive integer factors of 396 that divides 396 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396

Least Common Multiple of 390 and 396 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 390 and 396, than apply into the LCM equation.

GCF(390,396) = 6
LCM(390,396) = ( 390 × 396) / 6
LCM(390,396) = 154440 / 6
LCM(390,396) = 25740

Properties of LCM 390 and 396

(i) The LCM of 396 and 390 is associative

LCM of 390 and 396 = LCM of 396 and 390

Related Least Common Multiples of 390

Related Least Common Multiples of 396

Frequently Asked Questions on LCM of 390 and 396

1. What is the LCM of 390 and 396?

Answer: LCM of 390 and 396 is 25740.

2. What are the Factors of 390?

Answer: Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390. There are 16 integers that are factors of 390. The greatest factor of 390 is 390.

3. What are the Factors of 396?

Answer: Factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396. There are 18 integers that are factors of 396. The greatest factor of 396 is 396.

4. How to Find the LCM of 390 and 396?

Answer:

Least Common Multiple of 390 and 396 = 25740

Step 1: Find the prime factorization of 390

390 = 2 x 3 x 5 x 13

Step 2: Find the prime factorization of 396

396 = 2 x 2 x 3 x 3 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 = 25740 = 2 x 2 x 3 x 3 x 5 x 11 x 13

Step 4: Therefore, the least common multiple of 390 and 396 is 25740.