Least Common Multiple of 378 and 382

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 382 the smallest integer that is 72198 that is divisible by both numbers.

Least Common Multiple (LCM) of 378 and 382 is 72198.

LCM(378,382) = 72198

LCM of 378 and 382

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

LCM of:
and

Least Common Multiple of 378 and 382

LCM of 378 and 382 is 72198

Least common multiple can be found by multiplying the highest exponent prime factors of 378 and 382. First we will calculate the prime factors of 378 and 382.

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 382


2 382
191 191
1

Prime factors of 382 are 2,191. Prime factorization of 382 in exponential form is:

382 = 21×1911

Now multiplying the highest exponent prime factors to calculate the LCM of 378 and 382.

LCM(378,382) = 21×33×71×1911
LCM(378,382) = 72198

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 382

List of positive integer factors of 382 that divides 382 without a remainder.

1, 2, 191, 382

Least Common Multiple of 378 and 382 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 382, than apply into the LCM equation.

GCF(378,382) = 2
LCM(378,382) = ( 378 × 382) / 2
LCM(378,382) = 144396 / 2
LCM(378,382) = 72198

Properties of LCM 378 and 382

(i) The LCM of 382 and 378 is associative

LCM of 378 and 382 = LCM of 382 and 378

Related Least Common Multiples of 378

Related Least Common Multiples of 382

Frequently Asked Questions on LCM of 378 and 382

1. What is the LCM of 378 and 382?

Answer: LCM of 378 and 382 is 72198.

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 382?

Answer: Factors of 382 are 1, 2, 191, 382. There are 4 integers that are factors of 382. The greatest factor of 382 is 382.

4. How to Find the LCM of 378 and 382?

Answer:

Least Common Multiple of 378 and 382 = 72198

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 382

382 = 2 x 191

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

LCM = 72198 = 2 x 3 x 3 x 3 x 7 x 191

Step 4: Therefore, the least common multiple of 378 and 382 is 72198.