Least Common Multiple of 381 and 384

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 381 and 384 the smallest integer that is 48768 that is divisible by both numbers.

Least Common Multiple (LCM) of 381 and 384 is 48768.

LCM(381,384) = 48768

LCM of 381 and 384

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

LCM of:
and

Least Common Multiple of 381 and 384

LCM of 381 and 384 is 48768

Least common multiple can be found by multiplying the highest exponent prime factors of 381 and 384. First we will calculate the prime factors of 381 and 384.

Prime Factorization of 381


3 381
127 127
1

Prime factors of 381 are 3,127. Prime factorization of 381 in exponential form is:

381 = 31×1271

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

Now multiplying the highest exponent prime factors to calculate the LCM of 381 and 384.

LCM(381,384) = 27×31×1271
LCM(381,384) = 48768

Factors of 381

List of positive integer factors of 381 that divides 381 without a remainder.

1, 3, 127, 381

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

Least Common Multiple of 381 and 384 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 381 and 384, than apply into the LCM equation.

GCF(381,384) = 3
LCM(381,384) = ( 381 × 384) / 3
LCM(381,384) = 146304 / 3
LCM(381,384) = 48768

Properties of LCM 381 and 384

(i) The LCM of 384 and 381 is associative

LCM of 381 and 384 = LCM of 384 and 381

Related Least Common Multiples of 381

Related Least Common Multiples of 384

Frequently Asked Questions on LCM of 381 and 384

1. What is the LCM of 381 and 384?

Answer: LCM of 381 and 384 is 48768.

2. What are the Factors of 381?

Answer: Factors of 381 are 1, 3, 127, 381. There are 4 integers that are factors of 381. The greatest factor of 381 is 381.

3. 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.

4. How to Find the LCM of 381 and 384?

Answer:

Least Common Multiple of 381 and 384 = 48768

Step 1: Find the prime factorization of 381

381 = 3 x 127

Step 2: Find the prime factorization of 384

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

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

LCM = 48768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 127

Step 4: Therefore, the least common multiple of 381 and 384 is 48768.