Least Common Multiple of 378 and 380

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 380 the smallest integer that is 71820 that is divisible by both numbers.

Least Common Multiple (LCM) of 378 and 380 is 71820.

LCM(378,380) = 71820

LCM of 378 and 380

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

LCM of:
and

Least Common Multiple of 378 and 380

LCM of 378 and 380 is 71820

Least common multiple can be found by multiplying the highest exponent prime factors of 378 and 380. First we will calculate the prime factors of 378 and 380.

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 380


2 380
2 190
5 95
19 19
1

Prime factors of 380 are 2, 5,19. Prime factorization of 380 in exponential form is:

380 = 22×51×191

Now multiplying the highest exponent prime factors to calculate the LCM of 378 and 380.

LCM(378,380) = 22×33×51×71×191
LCM(378,380) = 71820

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 380

List of positive integer factors of 380 that divides 380 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380

Least Common Multiple of 378 and 380 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 380, than apply into the LCM equation.

GCF(378,380) = 2
LCM(378,380) = ( 378 × 380) / 2
LCM(378,380) = 143640 / 2
LCM(378,380) = 71820

Properties of LCM 378 and 380

(i) The LCM of 380 and 378 is associative

LCM of 378 and 380 = LCM of 380 and 378

Related Least Common Multiples of 378

Related Least Common Multiples of 380

Frequently Asked Questions on LCM of 378 and 380

1. What is the LCM of 378 and 380?

Answer: LCM of 378 and 380 is 71820.

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 380?

Answer: Factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380. There are 12 integers that are factors of 380. The greatest factor of 380 is 380.

4. How to Find the LCM of 378 and 380?

Answer:

Least Common Multiple of 378 and 380 = 71820

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 380

380 = 2 x 2 x 5 x 19

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

LCM = 71820 = 2 x 2 x 3 x 3 x 3 x 5 x 7 x 19

Step 4: Therefore, the least common multiple of 378 and 380 is 71820.