Least Common Multiple of 384 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 384 and 392 the smallest integer that is 18816 that is divisible by both numbers.

Least Common Multiple (LCM) of 384 and 392 is 18816.

LCM(384,392) = 18816

LCM of 384 and 392

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

LCM of:
and

Least Common Multiple of 384 and 392

LCM of 384 and 392 is 18816

Least common multiple can be found by multiplying the highest exponent prime factors of 384 and 392. First we will calculate the prime factors of 384 and 392.

Prime Factorization of 384


2 384
2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 384 are 2,3. Prime factorization of 384 in exponential form is:

384 = 27×31

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 384 and 392.

LCM(384,392) = 27×31×72
LCM(384,392) = 18816

Factors of 384

List of positive integer factors of 384 that divides 384 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384

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 384 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 384 and 392, than apply into the LCM equation.

GCF(384,392) = 8
LCM(384,392) = ( 384 × 392) / 8
LCM(384,392) = 150528 / 8
LCM(384,392) = 18816

Properties of LCM 384 and 392

(i) The LCM of 392 and 384 is associative

LCM of 384 and 392 = LCM of 392 and 384

Related Least Common Multiples of 384

Related Least Common Multiples of 392

Frequently Asked Questions on LCM of 384 and 392

1. What is the LCM of 384 and 392?

Answer: LCM of 384 and 392 is 18816.

2. What are the Factors of 384?

Answer: Factors of 384 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 384. There are 16 integers that are factors of 384. The greatest factor of 384 is 384.

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 384 and 392?

Answer:

Least Common Multiple of 384 and 392 = 18816

Step 1: Find the prime factorization of 384

384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

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 = 18816 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7 x 7

Step 4: Therefore, the least common multiple of 384 and 392 is 18816.