Least Common Multiple of 390 and 392

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 392 the smallest integer that is 76440 that is divisible by both numbers.

Least Common Multiple (LCM) of 390 and 392 is 76440.

LCM(390,392) = 76440

LCM of 390 and 392

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

LCM of:
and

Least Common Multiple of 390 and 392

LCM of 390 and 392 is 76440

Least common multiple can be found by multiplying the highest exponent prime factors of 390 and 392. First we will calculate the prime factors of 390 and 392.

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 392


2 392
2 196
2 98
7 49
7 7
1

Prime factors of 392 are 2,7. Prime factorization of 392 in exponential form is:

392 = 23×72

Now multiplying the highest exponent prime factors to calculate the LCM of 390 and 392.

LCM(390,392) = 23×31×51×72×131
LCM(390,392) = 76440

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 392

List of positive integer factors of 392 that divides 392 without a remainder.

1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392

Least Common Multiple of 390 and 392 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 392, than apply into the LCM equation.

GCF(390,392) = 2
LCM(390,392) = ( 390 × 392) / 2
LCM(390,392) = 152880 / 2
LCM(390,392) = 76440

Properties of LCM 390 and 392

(i) The LCM of 392 and 390 is associative

LCM of 390 and 392 = LCM of 392 and 390

Related Least Common Multiples of 390

Related Least Common Multiples of 392

Frequently Asked Questions on LCM of 390 and 392

1. What is the LCM of 390 and 392?

Answer: LCM of 390 and 392 is 76440.

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 392?

Answer: Factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392. There are 12 integers that are factors of 392. The greatest factor of 392 is 392.

4. How to Find the LCM of 390 and 392?

Answer:

Least Common Multiple of 390 and 392 = 76440

Step 1: Find the prime factorization of 390

390 = 2 x 3 x 5 x 13

Step 2: Find the prime factorization of 392

392 = 2 x 2 x 2 x 7 x 7

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

LCM = 76440 = 2 x 2 x 2 x 3 x 5 x 7 x 7 x 13

Step 4: Therefore, the least common multiple of 390 and 392 is 76440.