Least Common Multiple of 412 and 413

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 412 and 413 the smallest integer that is 170156 that is divisible by both numbers.

Least Common Multiple (LCM) of 412 and 413 is 170156.

LCM(412,413) = 170156

LCM of 412 and 413

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

LCM of:
and

Least Common Multiple of 412 and 413

LCM of 412 and 413 is 170156

Least common multiple can be found by multiplying the highest exponent prime factors of 412 and 413. First we will calculate the prime factors of 412 and 413.

Prime Factorization of 412


2 412
2 206
103 103
1

Prime factors of 412 are 2,103. Prime factorization of 412 in exponential form is:

412 = 22×1031

Prime Factorization of 413


7 413
59 59
1

Prime factors of 413 are 7,59. Prime factorization of 413 in exponential form is:

413 = 71×591

Now multiplying the highest exponent prime factors to calculate the LCM of 412 and 413.

LCM(412,413) = 22×71×591×1031
LCM(412,413) = 170156

Factors of 412

List of positive integer factors of 412 that divides 412 without a remainder.

1, 2, 4, 103, 206, 412

Factors of 413

List of positive integer factors of 413 that divides 413 without a remainder.

1, 7, 59, 413

Least Common Multiple of 412 and 413 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 412 and 413, than apply into the LCM equation.

GCF(412,413) = 1
LCM(412,413) = ( 412 × 413) / 1
LCM(412,413) = 170156 / 1
LCM(412,413) = 170156

Properties of LCM 412 and 413

(i) The LCM of 413 and 412 is associative

LCM of 412 and 413 = LCM of 413 and 412

Related Least Common Multiples of 412

Related Least Common Multiples of 413

Frequently Asked Questions on LCM of 412 and 413

1. What is the LCM of 412 and 413?

Answer: LCM of 412 and 413 is 170156.

2. What are the Factors of 412?

Answer: Factors of 412 are 1, 2, 4, 103, 206, 412. There are 6 integers that are factors of 412. The greatest factor of 412 is 412.

3. What are the Factors of 413?

Answer: Factors of 413 are 1, 7, 59, 413. There are 4 integers that are factors of 413. The greatest factor of 413 is 413.

4. How to Find the LCM of 412 and 413?

Answer:

Least Common Multiple of 412 and 413 = 170156

Step 1: Find the prime factorization of 412

412 = 2 x 2 x 103

Step 2: Find the prime factorization of 413

413 = 7 x 59

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

LCM = 170156 = 2 x 2 x 7 x 59 x 103

Step 4: Therefore, the least common multiple of 412 and 413 is 170156.