Least Common Multiple of 390 and 398

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 390 and 398 the smallest integer that is 77610 that is divisible by both numbers.

Least Common Multiple (LCM) of 390 and 398 is 77610.

LCM(390,398) = 77610

LCM of 390 and 398

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

LCM of:
and

Least Common Multiple of 390 and 398

LCM of 390 and 398 is 77610

Least common multiple can be found by multiplying the highest exponent prime factors of 390 and 398. First we will calculate the prime factors of 390 and 398.

Prime Factorization of 390


2 390
3 195
5 65
13 13
1

Prime factors of 390 are 2, 3, 5,13. Prime factorization of 390 in exponential form is:

390 = 21×31×51×131

Prime Factorization of 398


2 398
199 199
1

Prime factors of 398 are 2,199. Prime factorization of 398 in exponential form is:

398 = 21×1991

Now multiplying the highest exponent prime factors to calculate the LCM of 390 and 398.

LCM(390,398) = 21×31×51×131×1991
LCM(390,398) = 77610

Factors of 390

List of positive integer factors of 390 that divides 390 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390

Factors of 398

List of positive integer factors of 398 that divides 398 without a remainder.

1, 2, 199, 398

Least Common Multiple of 390 and 398 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 390 and 398, than apply into the LCM equation.

GCF(390,398) = 2
LCM(390,398) = ( 390 × 398) / 2
LCM(390,398) = 155220 / 2
LCM(390,398) = 77610

Properties of LCM 390 and 398

(i) The LCM of 398 and 390 is associative

LCM of 390 and 398 = LCM of 398 and 390

Related Least Common Multiples of 390

Related Least Common Multiples of 398

Frequently Asked Questions on LCM of 390 and 398

1. What is the LCM of 390 and 398?

Answer: LCM of 390 and 398 is 77610.

2. What are the Factors of 390?

Answer: Factors of 390 are 1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195, 390. There are 16 integers that are factors of 390. The greatest factor of 390 is 390.

3. What are the Factors of 398?

Answer: Factors of 398 are 1, 2, 199, 398. There are 4 integers that are factors of 398. The greatest factor of 398 is 398.

4. How to Find the LCM of 390 and 398?

Answer:

Least Common Multiple of 390 and 398 = 77610

Step 1: Find the prime factorization of 390

390 = 2 x 3 x 5 x 13

Step 2: Find the prime factorization of 398

398 = 2 x 199

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

LCM = 77610 = 2 x 3 x 5 x 13 x 199

Step 4: Therefore, the least common multiple of 390 and 398 is 77610.