Least Common Multiple of 8400 and 8401

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 8400 and 8401 the smallest integer that is 70568400 that is divisible by both numbers.

Least Common Multiple (LCM) of 8400 and 8401 is 70568400.

LCM(8400,8401) = 70568400

LCM of 8400 and 8401

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

LCM of:
and

Least Common Multiple of 8400 and 8401

LCM of 8400 and 8401 is 70568400

Least common multiple can be found by multiplying the highest exponent prime factors of 8400 and 8401. First we will calculate the prime factors of 8400 and 8401.

Prime Factorization of 8400


2 8400
2 4200
2 2100
2 1050
3 525
5 175
5 35
7 7
1

Prime factors of 8400 are 2, 3, 5,7. Prime factorization of 8400 in exponential form is:

8400 = 24×31×52×71

Prime Factorization of 8401


31 8401
271 271
1

Prime factors of 8401 are 31,271. Prime factorization of 8401 in exponential form is:

8401 = 311×2711

Now multiplying the highest exponent prime factors to calculate the LCM of 8400 and 8401.

LCM(8400,8401) = 24×31×52×71×311×2711
LCM(8400,8401) = 70568400

Factors of 8400

List of positive integer factors of 8400 that divides 8400 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400

Factors of 8401

List of positive integer factors of 8401 that divides 8401 without a remainder.

1, 31, 271, 8401

Least Common Multiple of 8400 and 8401 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8400 and 8401, than apply into the LCM equation.

GCF(8400,8401) = 1
LCM(8400,8401) = ( 8400 × 8401) / 1
LCM(8400,8401) = 70568400 / 1
LCM(8400,8401) = 70568400

Properties of LCM 8400 and 8401

(i) The LCM of 8401 and 8400 is associative

LCM of 8400 and 8401 = LCM of 8401 and 8400

Related Least Common Multiples of 8400

Related Least Common Multiples of 8401

Frequently Asked Questions on LCM of 8400 and 8401

1. What is the LCM of 8400 and 8401?

Answer: LCM of 8400 and 8401 is 70568400.

2. What are the Factors of 8400?

Answer: Factors of 8400 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400. There are 60 integers that are factors of 8400. The greatest factor of 8400 is 8400.

3. What are the Factors of 8401?

Answer: Factors of 8401 are 1, 31, 271, 8401. There are 4 integers that are factors of 8401. The greatest factor of 8401 is 8401.

4. How to Find the LCM of 8400 and 8401?

Answer:

Least Common Multiple of 8400 and 8401 = 70568400

Step 1: Find the prime factorization of 8400

8400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7

Step 2: Find the prime factorization of 8401

8401 = 31 x 271

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

LCM = 70568400 = 2 x 2 x 2 x 2 x 3 x 5 x 5 x 7 x 31 x 271

Step 4: Therefore, the least common multiple of 8400 and 8401 is 70568400.