Least Common Multiple of 378 and 381

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 378 and 381 the smallest integer that is 48006 that is divisible by both numbers.

Least Common Multiple (LCM) of 378 and 381 is 48006.

LCM(378,381) = 48006

LCM of 378 and 381

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

LCM of:
and

Least Common Multiple of 378 and 381

LCM of 378 and 381 is 48006

Least common multiple can be found by multiplying the highest exponent prime factors of 378 and 381. First we will calculate the prime factors of 378 and 381.

Prime Factorization of 378


2 378
3 189
3 63
3 21
7 7
1

Prime factors of 378 are 2, 3,7. Prime factorization of 378 in exponential form is:

378 = 21×33×71

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

Now multiplying the highest exponent prime factors to calculate the LCM of 378 and 381.

LCM(378,381) = 21×33×71×1271
LCM(378,381) = 48006

Factors of 378

List of positive integer factors of 378 that divides 378 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378

Factors of 381

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

1, 3, 127, 381

Least Common Multiple of 378 and 381 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 378 and 381, than apply into the LCM equation.

GCF(378,381) = 3
LCM(378,381) = ( 378 × 381) / 3
LCM(378,381) = 144018 / 3
LCM(378,381) = 48006

Properties of LCM 378 and 381

(i) The LCM of 381 and 378 is associative

LCM of 378 and 381 = LCM of 381 and 378

Related Least Common Multiples of 378

Related Least Common Multiples of 381

Frequently Asked Questions on LCM of 378 and 381

1. What is the LCM of 378 and 381?

Answer: LCM of 378 and 381 is 48006.

2. What are the Factors of 378?

Answer: Factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378. There are 16 integers that are factors of 378. The greatest factor of 378 is 378.

3. 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.

4. How to Find the LCM of 378 and 381?

Answer:

Least Common Multiple of 378 and 381 = 48006

Step 1: Find the prime factorization of 378

378 = 2 x 3 x 3 x 3 x 7

Step 2: Find the prime factorization of 381

381 = 3 x 127

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

LCM = 48006 = 2 x 3 x 3 x 3 x 7 x 127

Step 4: Therefore, the least common multiple of 378 and 381 is 48006.