Least Common Multiple of 398 and 400

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 400 the smallest integer that is 79600 that is divisible by both numbers.

Least Common Multiple (LCM) of 398 and 400 is 79600.

LCM(398,400) = 79600

LCM of 398 and 400

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

LCM of:
and

Least Common Multiple of 398 and 400

LCM of 398 and 400 is 79600

Least common multiple can be found by multiplying the highest exponent prime factors of 398 and 400. First we will calculate the prime factors of 398 and 400.

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 400


2 400
2 200
2 100
2 50
5 25
5 5
1

Prime factors of 400 are 2,5. Prime factorization of 400 in exponential form is:

400 = 24×52

Now multiplying the highest exponent prime factors to calculate the LCM of 398 and 400.

LCM(398,400) = 24×52×1991
LCM(398,400) = 79600

Factors of 398

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

1, 2, 199, 398

Factors of 400

List of positive integer factors of 400 that divides 400 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

Least Common Multiple of 398 and 400 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 400, than apply into the LCM equation.

GCF(398,400) = 2
LCM(398,400) = ( 398 × 400) / 2
LCM(398,400) = 159200 / 2
LCM(398,400) = 79600

Properties of LCM 398 and 400

(i) The LCM of 400 and 398 is associative

LCM of 398 and 400 = LCM of 400 and 398

Related Least Common Multiples of 398

Related Least Common Multiples of 400

Frequently Asked Questions on LCM of 398 and 400

1. What is the LCM of 398 and 400?

Answer: LCM of 398 and 400 is 79600.

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 400?

Answer: Factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. There are 15 integers that are factors of 400. The greatest factor of 400 is 400.

4. How to Find the LCM of 398 and 400?

Answer:

Least Common Multiple of 398 and 400 = 79600

Step 1: Find the prime factorization of 398

398 = 2 x 199

Step 2: Find the prime factorization of 400

400 = 2 x 2 x 2 x 2 x 5 x 5

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

LCM = 79600 = 2 x 2 x 2 x 2 x 5 x 5 x 199

Step 4: Therefore, the least common multiple of 398 and 400 is 79600.