Least Common Multiple of 398 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 398 and 406 the smallest integer that is 80794 that is divisible by both numbers.

Least Common Multiple (LCM) of 398 and 406 is 80794.

LCM(398,406) = 80794

LCM of 398 and 406

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

LCM of:
and

Least Common Multiple of 398 and 406

LCM of 398 and 406 is 80794

Least common multiple can be found by multiplying the highest exponent prime factors of 398 and 406. First we will calculate the prime factors of 398 and 406.

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

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 398 and 406.

LCM(398,406) = 21×71×291×1991
LCM(398,406) = 80794

Factors of 398

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

1, 2, 199, 398

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 398 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 398 and 406, than apply into the LCM equation.

GCF(398,406) = 2
LCM(398,406) = ( 398 × 406) / 2
LCM(398,406) = 161588 / 2
LCM(398,406) = 80794

Properties of LCM 398 and 406

(i) The LCM of 406 and 398 is associative

LCM of 398 and 406 = LCM of 406 and 398

Related Least Common Multiples of 398

Related Least Common Multiples of 406

Frequently Asked Questions on LCM of 398 and 406

1. What is the LCM of 398 and 406?

Answer: LCM of 398 and 406 is 80794.

2. 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.

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 398 and 406?

Answer:

Least Common Multiple of 398 and 406 = 80794

Step 1: Find the prime factorization of 398

398 = 2 x 199

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 = 80794 = 2 x 7 x 29 x 199

Step 4: Therefore, the least common multiple of 398 and 406 is 80794.