Least Common Multiple of 399 and 406

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 399 and 406 the smallest integer that is 23142 that is divisible by both numbers.

Least Common Multiple (LCM) of 399 and 406 is 23142.

LCM(399,406) = 23142

LCM of 399 and 406

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

LCM of:
and

Least Common Multiple of 399 and 406

LCM of 399 and 406 is 23142

Least common multiple can be found by multiplying the highest exponent prime factors of 399 and 406. First we will calculate the prime factors of 399 and 406.

Prime Factorization of 399


3 399
7 133
19 19
1

Prime factors of 399 are 3, 7,19. Prime factorization of 399 in exponential form is:

399 = 31×71×191

Prime Factorization of 406


2 406
7 203
29 29
1

Prime factors of 406 are 2, 7,29. Prime factorization of 406 in exponential form is:

406 = 21×71×291

Now multiplying the highest exponent prime factors to calculate the LCM of 399 and 406.

LCM(399,406) = 21×31×71×191×291
LCM(399,406) = 23142

Factors of 399

List of positive integer factors of 399 that divides 399 without a remainder.

1, 3, 7, 19, 21, 57, 133, 399

Factors of 406

List of positive integer factors of 406 that divides 406 without a remainder.

1, 2, 7, 14, 29, 58, 203, 406

Least Common Multiple of 399 and 406 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 399 and 406, than apply into the LCM equation.

GCF(399,406) = 7
LCM(399,406) = ( 399 × 406) / 7
LCM(399,406) = 161994 / 7
LCM(399,406) = 23142

Properties of LCM 399 and 406

(i) The LCM of 406 and 399 is associative

LCM of 399 and 406 = LCM of 406 and 399

Related Least Common Multiples of 399

Related Least Common Multiples of 406

Frequently Asked Questions on LCM of 399 and 406

1. What is the LCM of 399 and 406?

Answer: LCM of 399 and 406 is 23142.

2. What are the Factors of 399?

Answer: Factors of 399 are 1, 3, 7, 19, 21, 57, 133, 399. There are 8 integers that are factors of 399. The greatest factor of 399 is 399.

3. What are the Factors of 406?

Answer: Factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406. There are 8 integers that are factors of 406. The greatest factor of 406 is 406.

4. How to Find the LCM of 399 and 406?

Answer:

Least Common Multiple of 399 and 406 = 23142

Step 1: Find the prime factorization of 399

399 = 3 x 7 x 19

Step 2: Find the prime factorization of 406

406 = 2 x 7 x 29

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

LCM = 23142 = 2 x 3 x 7 x 19 x 29

Step 4: Therefore, the least common multiple of 399 and 406 is 23142.