Least Common Multiple of 412 and 417

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 417 the smallest integer that is 171804 that is divisible by both numbers.

Least Common Multiple (LCM) of 412 and 417 is 171804.

LCM(412,417) = 171804

LCM of 412 and 417

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

LCM of:
and

Least Common Multiple of 412 and 417

LCM of 412 and 417 is 171804

Least common multiple can be found by multiplying the highest exponent prime factors of 412 and 417. First we will calculate the prime factors of 412 and 417.

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 417


3 417
139 139
1

Prime factors of 417 are 3,139. Prime factorization of 417 in exponential form is:

417 = 31×1391

Now multiplying the highest exponent prime factors to calculate the LCM of 412 and 417.

LCM(412,417) = 22×31×1031×1391
LCM(412,417) = 171804

Factors of 412

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

1, 2, 4, 103, 206, 412

Factors of 417

List of positive integer factors of 417 that divides 417 without a remainder.

1, 3, 139, 417

Least Common Multiple of 412 and 417 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 417, than apply into the LCM equation.

GCF(412,417) = 1
LCM(412,417) = ( 412 × 417) / 1
LCM(412,417) = 171804 / 1
LCM(412,417) = 171804

Properties of LCM 412 and 417

(i) The LCM of 417 and 412 is associative

LCM of 412 and 417 = LCM of 417 and 412

Related Least Common Multiples of 412

Related Least Common Multiples of 417

Frequently Asked Questions on LCM of 412 and 417

1. What is the LCM of 412 and 417?

Answer: LCM of 412 and 417 is 171804.

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 417?

Answer: Factors of 417 are 1, 3, 139, 417. There are 4 integers that are factors of 417. The greatest factor of 417 is 417.

4. How to Find the LCM of 412 and 417?

Answer:

Least Common Multiple of 412 and 417 = 171804

Step 1: Find the prime factorization of 412

412 = 2 x 2 x 103

Step 2: Find the prime factorization of 417

417 = 3 x 139

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

LCM = 171804 = 2 x 2 x 3 x 103 x 139

Step 4: Therefore, the least common multiple of 412 and 417 is 171804.